Electric Dipole - Revision history

Pbrowne7: /* Electric Dipoles in Life */

2025-04-14T03:27:29Z

Electric Dipoles in Life

← Older revision		Revision as of 23:27, 13 April 2025
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	To specifically Biomedical Engineering, dipole interactions can help break down molecules as a result of ion polarization and separation.		To specifically Biomedical Engineering, dipole interactions can help break down molecules as a result of ion polarization and separation.

	==Electric Dipoles in ~~Life~~==		==Electric Dipoles in Nature==
	Beyond the applications talked about with dipoles previously, we can use electric dipoles to observe the fundamental symmetries of nature. Permanent electric dipole moments or (EDM) in particles such as electrons and neutrons are a powerful tool that is used to test violations of time-reversal and charge-parity symmetries. These two phenomena are keys to explaining the imbalance between matter and antimatter in the cosmos. A permanent electric dipole moment is the fixed spatial separation between a positive and negative charge in a system. This imbalance indicates an electric polarity. EDM is a vector that has both size and orientation and is a fundamental property of atoms, particles, and molecules.		Beyond the applications talked about with dipoles previously, we can use electric dipoles to observe the fundamental symmetries of nature. Permanent electric dipole moments or (EDM) in particles such as electrons and neutrons are a powerful tool that is used to test violations of time-reversal and charge-parity symmetries. These two phenomena are keys to explaining the imbalance between matter and antimatter in the cosmos. A permanent electric dipole moment is the fixed spatial separation between a positive and negative charge in a system. This imbalance indicates an electric polarity. EDM is a vector that has both size and orientation and is a fundamental property of atoms, particles, and molecules.

Pbrowne7 at 03:27, 14 April 2025

2025-04-14T03:27:08Z

← Older revision		Revision as of 23:27, 13 April 2025
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	To specifically Biomedical Engineering, dipole interactions can help break down molecules as a result of ion polarization and separation.		To specifically Biomedical Engineering, dipole interactions can help break down molecules as a result of ion polarization and separation.

			==Electric Dipoles in Life==
			Beyond the applications talked about with dipoles previously, we can use electric dipoles to observe the fundamental symmetries of nature. Permanent electric dipole moments or (EDM) in particles such as electrons and neutrons are a powerful tool that is used to test violations of time-reversal and charge-parity symmetries. These two phenomena are keys to explaining the imbalance between matter and antimatter in the cosmos. A permanent electric dipole moment is the fixed spatial separation between a positive and negative charge in a system. This imbalance indicates an electric polarity. EDM is a vector that has both size and orientation and is a fundamental property of atoms, particles, and molecules.

	==History==		==History==

Pbrowne7 at 03:11, 14 April 2025

2025-04-14T03:11:59Z

← Older revision		Revision as of 23:11, 13 April 2025
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	'''Claimed By: ~~Qufei Hou~~'''		'''Claimed By: Preston Browne'''

	==Summary==		==Summary==
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	[[File:dipole_torque_2.gif]]		[[File:dipole_torque_2.gif]]

	Note how the electric field will exert an an electric force on each of the point charges. Since the electric field is uniform and charge of each point charge is equal and opposite, the electric force exerted on each point charge will be equal and opposite. The magnitude of each force is simply the force on a point charge, or <math> F = qE </math>. The component of this force perpendicular to the dipole axis can be written as <math> F_{\bot}= qE\sin \theta</math>, where theta is the angle between the electric field and the dipole. It is this perpendicular force which causes rotational motion, and thus is the force component of the applied torque. Since the forces are separated by the distance of the dipole, it can be generalized that an electric field produces the following torque on an electric dipole:		Note how the electric field will exert an an electric force on each of the point charges. Since the electric field is uniform and charge of each point charge is equal and opposite, the electric force exerted on each point charge will be equal and opposite. The torque works to align the dipole with the electric field. The magnitude of each force is simply the force on a point charge, or <math> F = qE </math>. The component of this force perpendicular to the dipole axis can be written as <math> F_{\bot}= qE\sin \theta</math>, where theta is the angle between the electric field and the dipole. It is this perpendicular force which causes rotational motion, and thus is the force component of the applied torque. Since the forces are separated by the distance of the dipole, it can be generalized that an electric field produces the following torque on an electric dipole:

	<math> \tau\ = p \times E = Eqd\sin\theta</math>		<math> \tau\ = p \times E = Eqd\sin\theta</math>

Qhou9: /* Summary */

2023-04-17T01:12:46Z

Summary

← Older revision		Revision as of 21:12, 16 April 2023
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	A dipole can be created, for example, when you place a neutral atom in an electric field, because of the movement of electrons, the atom polarizes (negative charge on one side, positive charge on the other) and yields a separation of charge.		A dipole can be created, for example, when you place a neutral atom in an electric field, because of the movement of electrons, the atom polarizes (negative charge on one side, positive charge on the other) and yields a separation of charge.

			Electric dipole can be characterized by its dipole moment, which is a measure of the separation of positive and negative electrical charges within a system.
			Two point charges, one with charge +q and the other one with charge −q separated by a distance d, constitute an electric dipole. The magnitude of the dipole moment is:

			p = qd

	A prime example of this is the molecule for water, which forms a 105 degree angle between the two hydrogens connected to the oxygen. Since the oxygen has a greater electronegativity, it pulls more strongly on the electrons shared by the oxygen and hydrogen atoms and that end of the molecule becomes more negatively charged compared to the hydrogen end. Therefore, the net electric dipole points towards the oxygen atom.		A prime example of this is the molecule for water, which forms a 105 degree angle between the two hydrogens connected to the oxygen. Since the oxygen has a greater electronegativity, it pulls more strongly on the electrons shared by the oxygen and hydrogen atoms and that end of the molecule becomes more negatively charged compared to the hydrogen end. Therefore, the net electric dipole points towards the oxygen atom.

Qhou9 at 01:07, 17 April 2023

2023-04-17T01:07:32Z

← Older revision		Revision as of 21:07, 16 April 2023
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			'''Claimed By: Qufei Hou'''

	==Summary==		==Summary==

	~~'''Claimed By: Qufei Hou'''~~

	An electric dipole is made up of two point charges that have equal but opposite electric charges (q) and are separated by a short distance (d).		An electric dipole is made up of two point charges that have equal but opposite electric charges (q) and are separated by a short distance (d).

Qhou9 at 01:07, 17 April 2023

2023-04-17T01:07:13Z

← Older revision		Revision as of 21:07, 16 April 2023
Line 1:		Line 1:

	==Summary==		==Summary==

			'''Claimed By: Qufei Hou'''

	An electric dipole is made up of two point charges that have equal but opposite electric charges (q) and are separated by a short distance (d).		An electric dipole is made up of two point charges that have equal but opposite electric charges (q) and are separated by a short distance (d).

William.nguyen: /* An Exact Model */

2022-07-25T15:19:14Z

An Exact Model

← Older revision		Revision as of 11:19, 25 July 2022
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	<math>\theta_+</math> and its counterpart <math>\theta_-</math> are not known. However, we can calculate them. We know <math>\theta_+</math> is formed by a triangle with one side length <math>p_y</math> and one side length <math>p_x - \frac{d}{2}</math>. Then <math>sin(\theta_+) = \frac{p_y}{\sqrt{(p_x - \frac{d}{2})^2+p_y^2}}</math>, from which you can calculate the angle. This looks disgusting, but a close inspection shows that <math>p_y</math> is the opposite side of the triangle, and the denominator is an expression forming the hypotenuse of the triangle (<math>r_+</math>) from known quantities. A similar method shows that <math>sin(\theta_-) = \frac{p_y}{\sqrt{(p_x + \frac{d}{2})^2+p_y^2}}</math>, where once again <math>\sqrt{(p_x + \frac{d}{2})^2+p_y^2} = \|\vec r_-\|</math>.		<math>\theta_+</math> and its counterpart <math>\theta_-</math> are not known. However, we can calculate them. We know <math>\theta_+</math> is formed by a triangle with one side length <math>p_y</math> and one side length <math>p_x - \frac{d}{2}</math>. Then <math>sin(\theta_+) = \frac{p_y}{\sqrt{(p_x - \frac{d}{2})^2+p_y^2}}</math>, from which you can calculate the angle. This looks disgusting, but a close inspection shows that <math>p_y</math> is the opposite side of the triangle, and the denominator is an expression forming the hypotenuse of the triangle (<math>r_+</math>) from known quantities. A similar method shows that <math>sin(\theta_-) = \frac{p_y}{\sqrt{(p_x + \frac{d}{2})^2+p_y^2}}</math>, where once again <math>\sqrt{(p_x + \frac{d}{2})^2+p_y^2} = \|\vec r_-\|</math>.

	We now have values for <math> d, q, \theta_+, \theta_-, \vec r_+, \vec r_-</math>. This is enough to calculate <math>E_{net}</math> in both directions. The general formula for electric field strength from a [[Point Charge]] is <math>E = \frac{1}{4\pi\epsilon_0} \frac{q}{\|\vec r\|^2} \hat r</math>. Then <math>\|E_+\| = \frac{1}{4\pi\epsilon_0} \frac{q_+}{\|\vec r_+\|^2}</math> and <math>\|E_-\| = \frac{1}{4\pi\epsilon_0} \frac{q_-}{\|\vec r_-\|^2}</math>. We want solely the magnitude in this case because we can calculate direction and component forces using sin and cosine. ~~Its~~ worth noting that we can expand <math>r_+, r_-</math> to the form in the denominator of the sine and cosine. We will use this later.		We now have values for <math> d, q, \theta_+, \theta_-, \vec r_+, \vec r_-</math>. This is enough to calculate <math>E_{net}</math> in both directions. The general formula for electric field strength from a [[Point Charge]] is <math>E = \frac{1}{4\pi\epsilon_0} \frac{q}{\|\vec r\|^2} \hat r</math>. Then <math>\|E_+\| = \frac{1}{4\pi\epsilon_0} \frac{q_+}{\|\vec r_+\|^2}</math> and <math>\|E_-\| = \frac{1}{4\pi\epsilon_0} \frac{q_-}{\|\vec r_-\|^2}</math>. We want solely the magnitude in this case because we can calculate direction and component forces using sin and cosine. It's worth noting that we can expand <math>r_+, r_-</math> to the form in the denominator of the sine and cosine. We will use this later.

	First we calculate <math>E_{net_y}</math>. <math>E_{net_y} = E_{+_y} + E_{-_y} = \frac{1}{4\pi\epsilon_0} \frac{q_+}{\|\vec r_+\|^2} sin(\theta_+) + \frac{1}{4\pi\epsilon_0} \frac{q_-}{\|\vec r_-\|^2} sin(\theta_-)</math>.		First we calculate <math>E_{net_y}</math>. <math>E_{net_y} = E_{+_y} + E_{-_y} = \frac{1}{4\pi\epsilon_0} \frac{q_+}{\|\vec r_+\|^2} sin(\theta_+) + \frac{1}{4\pi\epsilon_0} \frac{q_-}{\|\vec r_-\|^2} sin(\theta_-)</math>.

William.nguyen: /* Mathematical Models */

2022-07-25T15:14:35Z

Mathematical Models

← Older revision		Revision as of 11:14, 25 July 2022
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	An electric dipole is constructed from two point charges, one at position <math>[\frac{d}{2}, 0]</math> and one at position <math>[\frac{-d}{2}, 0]</math>. These point charges are of equal and opposite charge. We then wish to know the electric field due to the dipole at some point <math>p</math> in the plane (see the figure). <math>p</math> can be considered either a distance <math>[x_0, y_0]</math> from the midpoint of the dipole, or a distance <math>r</math> and an angle <math>\theta</math> as in the diagram.		An electric dipole is constructed from two point charges, one at position <math>[\frac{d}{2}, 0]</math> and one at position <math>[\frac{-d}{2}, 0]</math>. These point charges are of equal and opposite charge. We then wish to know the electric field due to the dipole at some point <math>p</math> in the plane (see the figure). <math>p</math> can be considered either a distance <math>[x_0, y_0]</math> from the midpoint of the dipole, or a distance <math>r</math> and an angle <math>\theta</math> as in the diagram.

	We state that the net electric field at <math>p</math> is <math>E_{net}</math> and has an x and y component, <math>E_{net_x}</math> and <math>E_{net_y}</math>. Then we can individually calculate the x and y components. First we realize that since <math>E_{net} = E_{q_+} + E_{q_-}</math>, <math>E_{net_x} = E_{q_{+x}} + E_{q_{-x}}</math>, similarly, for y, <math>E_{net_y} = E_{q_{+y}} + E_{q_{-y}}</math>. At this point, ~~its~~ worth noting that <math>E_{q_{+y}} = E_{q_+} * cos(\theta_+)</math>, where <math>\theta_+</math> is the angle from <math>q_{+}</math> to <math>p</math>.		We state that the net electric field at <math>p</math> is <math>E_{net}</math> and has an x and y component, <math>E_{net_x}</math> and <math>E_{net_y}</math>. Then we can individually calculate the x and y components. First we realize that since <math>E_{net} = E_{q_+} + E_{q_-}</math>, <math>E_{net_x} = E_{q_{+x}} + E_{q_{-x}}</math>, similarly, for y, <math>E_{net_y} = E_{q_{+y}} + E_{q_{-y}}</math>. At this point, it's worth noting that <math>E_{q_{+y}} = E_{q_+} * cos(\theta_+)</math>, where <math>\theta_+</math> is the angle from <math>q_{+}</math> to <math>p</math>.

	<math>\theta_+</math> and its counterpart <math>\theta_-</math> are not known. However, we can calculate them. We know <math>\theta_+</math> is formed by a triangle with one side length <math>p_y</math> and one side length <math>p_x - \frac{d}{2}</math>. Then <math>sin(\theta_+) = \frac{p_y}{\sqrt{(p_x - \frac{d}{2})^2+p_y^2}}</math>, from which you can calculate the angle. This looks disgusting, but a close inspection shows that <math>p_y</math> is the opposite side of the triangle, and the denominator is an expression forming the hypotenuse of the triangle (<math>r_+</math>) from known quantities. A similar method shows that <math>sin(\theta_-) = \frac{p_y}{\sqrt{(p_x + \frac{d}{2})^2+p_y^2}}</math>, where once again <math>\sqrt{(p_x + \frac{d}{2})^2+p_y^2} = \|\vec r_-\|</math>.		<math>\theta_+</math> and its counterpart <math>\theta_-</math> are not known. However, we can calculate them. We know <math>\theta_+</math> is formed by a triangle with one side length <math>p_y</math> and one side length <math>p_x - \frac{d}{2}</math>. Then <math>sin(\theta_+) = \frac{p_y}{\sqrt{(p_x - \frac{d}{2})^2+p_y^2}}</math>, from which you can calculate the angle. This looks disgusting, but a close inspection shows that <math>p_y</math> is the opposite side of the triangle, and the denominator is an expression forming the hypotenuse of the triangle (<math>r_+</math>) from known quantities. A similar method shows that <math>sin(\theta_-) = \frac{p_y}{\sqrt{(p_x + \frac{d}{2})^2+p_y^2}}</math>, where once again <math>\sqrt{(p_x + \frac{d}{2})^2+p_y^2} = \|\vec r_-\|</math>.

William.nguyen: /* Mathematical Models */

2022-07-25T15:14:16Z

Mathematical Models

← Older revision		Revision as of 11:14, 25 July 2022
Line 21:		Line 21:
	An electric dipole is constructed from two point charges, one at position <math>[\frac{d}{2}, 0]</math> and one at position <math>[\frac{-d}{2}, 0]</math>. These point charges are of equal and opposite charge. We then wish to know the electric field due to the dipole at some point <math>p</math> in the plane (see the figure). <math>p</math> can be considered either a distance <math>[x_0, y_0]</math> from the midpoint of the dipole, or a distance <math>r</math> and an angle <math>\theta</math> as in the diagram.		An electric dipole is constructed from two point charges, one at position <math>[\frac{d}{2}, 0]</math> and one at position <math>[\frac{-d}{2}, 0]</math>. These point charges are of equal and opposite charge. We then wish to know the electric field due to the dipole at some point <math>p</math> in the plane (see the figure). <math>p</math> can be considered either a distance <math>[x_0, y_0]</math> from the midpoint of the dipole, or a distance <math>r</math> and an angle <math>\theta</math> as in the diagram.

	We state that the net electric field at <math>p</math> is <math>E_{net}</math> and has an x and y component, <math>E_{net_x}</math> and <math>E_{net_y}</math>. Then we can individually calculate the x and y components. First we realize that since <math>E_{net} = E_{q_+} + E_{q_-}</math>, <math>E_{net_x} = E_{q_{+x}} + E_{q_{-x}}</math>, similarly for y <math>E_{net_y} = E_{q_{+y}} + E_{q_{-y}}</math>. At this point, its worth noting that <math>E_{q_{+y}} = E_{q_+} * cos(\theta_+)</math>, where <math>\theta_+</math> is the angle from <math>q_{+}</math> to <math>p</math>.		We state that the net electric field at <math>p</math> is <math>E_{net}</math> and has an x and y component, <math>E_{net_x}</math> and <math>E_{net_y}</math>. Then we can individually calculate the x and y components. First we realize that since <math>E_{net} = E_{q_+} + E_{q_-}</math>, <math>E_{net_x} = E_{q_{+x}} + E_{q_{-x}}</math>, similarly, for y, <math>E_{net_y} = E_{q_{+y}} + E_{q_{-y}}</math>. At this point, its worth noting that <math>E_{q_{+y}} = E_{q_+} * cos(\theta_+)</math>, where <math>\theta_+</math> is the angle from <math>q_{+}</math> to <math>p</math>.

	<math>\theta_+</math> and its counterpart <math>\theta_-</math> are not known. However, we can calculate them. We know <math>\theta_+</math> is formed by a triangle with one side length <math>p_y</math> and one side length <math>p_x - \frac{d}{2}</math>. Then <math>sin(\theta_+) = \frac{p_y}{\sqrt{(p_x - \frac{d}{2})^2+p_y^2}}</math>, from which you can calculate the angle. This looks disgusting, but a close inspection shows that <math>p_y</math> is the opposite side of the triangle, and the denominator is an expression forming the hypotenuse of the triangle (<math>r_+</math>) from known quantities. A similar method shows that <math>sin(\theta_-) = \frac{p_y}{\sqrt{(p_x + \frac{d}{2})^2+p_y^2}}</math>, where once again <math>\sqrt{(p_x + \frac{d}{2})^2+p_y^2} = \|\vec r_-\|</math>.		<math>\theta_+</math> and its counterpart <math>\theta_-</math> are not known. However, we can calculate them. We know <math>\theta_+</math> is formed by a triangle with one side length <math>p_y</math> and one side length <math>p_x - \frac{d}{2}</math>. Then <math>sin(\theta_+) = \frac{p_y}{\sqrt{(p_x - \frac{d}{2})^2+p_y^2}}</math>, from which you can calculate the angle. This looks disgusting, but a close inspection shows that <math>p_y</math> is the opposite side of the triangle, and the denominator is an expression forming the hypotenuse of the triangle (<math>r_+</math>) from known quantities. A similar method shows that <math>sin(\theta_-) = \frac{p_y}{\sqrt{(p_x + \frac{d}{2})^2+p_y^2}}</math>, where once again <math>\sqrt{(p_x + \frac{d}{2})^2+p_y^2} = \|\vec r_-\|</math>.

William.nguyen: /* Summary */

2022-07-25T15:04:51Z

Summary

← Older revision		Revision as of 11:04, 25 July 2022
Line 6:		Line 6:
	[[File:dipo.jpg\|An Electric Dipole]]		[[File:dipo.jpg\|An Electric Dipole]]

	The electric field is proportional to the cube of the distance from the dipole, and is dependent on whether you’re moving along the line separating the two charges or perpendicular to it.		The electric field is inversely proportional to the cube of the distance from the dipole, and is dependent on whether you’re moving along the line separating the two charges or perpendicular to it.

	A dipole can be created, for example, when you place a neutral atom in an electric field, because of the movement of electrons, the atom polarizes (negative charge on one side, positive charge on the other) and yields a separation of charge.		A dipole can be created, for example, when you place a neutral atom in an electric field, because of the movement of electrons, the atom polarizes (negative charge on one side, positive charge on the other) and yields a separation of charge.

← Older revision		Revision as of 11:19, 25 July 2022
Line 25:		Line 25:
	<math>\theta_+</math> and its counterpart <math>\theta_-</math> are not known. However, we can calculate them. We know <math>\theta_+</math> is formed by a triangle with one side length <math>p_y</math> and one side length <math>p_x - \frac{d}{2}</math>. Then <math>sin(\theta_+) = \frac{p_y}{\sqrt{(p_x - \frac{d}{2})^2+p_y^2}}</math>, from which you can calculate the angle. This looks disgusting, but a close inspection shows that <math>p_y</math> is the opposite side of the triangle, and the denominator is an expression forming the hypotenuse of the triangle (<math>r_+</math>) from known quantities. A similar method shows that <math>sin(\theta_-) = \frac{p_y}{\sqrt{(p_x + \frac{d}{2})^2+p_y^2}}</math>, where once again <math>\sqrt{(p_x + \frac{d}{2})^2+p_y^2} = \|\vec r_-\|</math>.		<math>\theta_+</math> and its counterpart <math>\theta_-</math> are not known. However, we can calculate them. We know <math>\theta_+</math> is formed by a triangle with one side length <math>p_y</math> and one side length <math>p_x - \frac{d}{2}</math>. Then <math>sin(\theta_+) = \frac{p_y}{\sqrt{(p_x - \frac{d}{2})^2+p_y^2}}</math>, from which you can calculate the angle. This looks disgusting, but a close inspection shows that <math>p_y</math> is the opposite side of the triangle, and the denominator is an expression forming the hypotenuse of the triangle (<math>r_+</math>) from known quantities. A similar method shows that <math>sin(\theta_-) = \frac{p_y}{\sqrt{(p_x + \frac{d}{2})^2+p_y^2}}</math>, where once again <math>\sqrt{(p_x + \frac{d}{2})^2+p_y^2} = \|\vec r_-\|</math>.

	We now have values for <math> d, q, \theta_+, \theta_-, \vec r_+, \vec r_-</math>. This is enough to calculate <math>E_{net}</math> in both directions. The general formula for electric field strength from a [[Point Charge]] is <math>E = \frac{1}{4\pi\epsilon_0} \frac{q}{\|\vec r\|^2} \hat r</math>. Then <math>\|E_+\| = \frac{1}{4\pi\epsilon_0} \frac{q_+}{\|\vec r_+\|^2}</math> and <math>\|E_-\| = \frac{1}{4\pi\epsilon_0} \frac{q_-}{\|\vec r_-\|^2}</math>. We want solely the magnitude in this case because we can calculate direction and component forces using sin and cosine. ~~Its~~ worth noting that we can expand <math>r_+, r_-</math> to the form in the denominator of the sine and cosine. We will use this later.		We now have values for <math> d, q, \theta_+, \theta_-, \vec r_+, \vec r_-</math>. This is enough to calculate <math>E_{net}</math> in both directions. The general formula for electric field strength from a [[Point Charge]] is <math>E = \frac{1}{4\pi\epsilon_0} \frac{q}{\|\vec r\|^2} \hat r</math>. Then <math>\|E_+\| = \frac{1}{4\pi\epsilon_0} \frac{q_+}{\|\vec r_+\|^2}</math> and <math>\|E_-\| = \frac{1}{4\pi\epsilon_0} \frac{q_-}{\|\vec r_-\|^2}</math>. We want solely the magnitude in this case because we can calculate direction and component forces using sin and cosine. It's worth noting that we can expand <math>r_+, r_-</math> to the form in the denominator of the sine and cosine. We will use this later.

	First we calculate <math>E_{net_y}</math>. <math>E_{net_y} = E_{+_y} + E_{-_y} = \frac{1}{4\pi\epsilon_0} \frac{q_+}{\|\vec r_+\|^2} sin(\theta_+) + \frac{1}{4\pi\epsilon_0} \frac{q_-}{\|\vec r_-\|^2} sin(\theta_-)</math>.		First we calculate <math>E_{net_y}</math>. <math>E_{net_y} = E_{+_y} + E_{-_y} = \frac{1}{4\pi\epsilon_0} \frac{q_+}{\|\vec r_+\|^2} sin(\theta_+) + \frac{1}{4\pi\epsilon_0} \frac{q_-}{\|\vec r_-\|^2} sin(\theta_-)</math>.