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• #### Daily Analysis: 24th October 2020

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Lesson 2, Topic 4
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# Electric Field Due to a Dipole

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Two charges 10?C are placed 5.0mm apart.Determine the electric field at a point P on the axis of the dipole 15 cm away from its centre O on the side of the positive charge.
Solution:
Field at P due to charge +10?C:
=4?(8.854×10?12C2N?1m?2)10?5?×(15?0.25)2×10?4m21?
=4.13×106NC?1 along BP
Field at P due to charge ?10?C
=4?(8.854×10?12C2N?1m?2)10?5?×(15+0.25)2×10?4m21?
=3.86×106NC?1 along PA
The resultant electric field at P due to the two charges at A and B is
=2.7×105NC?1 along BP.
In this example, the ratio OP/OB is quite large (= 60). Thus, we can expect to get approximately the same result as above by directly using the formula for electric field at a far-away point on the axis of a dipole.For a dipole consisting of charges q,2a distance apart, the electric field at a distance r from the centre on the axis of the dipole has a magnitude
E=4??0?r32p?(r/a>>1)
where p=2aq is the magnitude of the dipole moment.The direction of electric field on the dipole axis is always along the direction of the dipole moment vector (i.e., from ?q to q). Here,
p=10?5C×5×10?3m=5×10?8Cm
E=2.6×105NC?1
Along the dipole moment direction AB, which is close to the result obtained earlier.

##### ELECTRIC FIELD OF AN ELECTRIC DIPOLE FOR EQUATORIAL POINTS – EXAMPLE

Two charges each of 10 C are placed 5.0 mm apart.Determine the electric field at a point Q, 15 cm away from O on a line passing through O and normal to the axis of the dipole,
E=4??0?r3p?(r/a>>1)
=4?×(8.854×10?12C2N?1m?2)5×10?8?×(15)3×10?6m31?
=1.33×105NC?1
The direction of electric field in this case is opposite to the direction of the dipole moment vector.

##### ELECTRIC FIELD DUE TO A DIPOLE – FORMULA

E=4??0?1?r3p?3cos2?+1?
where ? is the  angle between the distance vector and dipole.

##### POTENTIAL DUE TO A DIPOLE AT A GENERAL POINT – DEFINITION

Potential due to a dipole is given by:
V?4??o?r2pcos??
where
p: electric dipole moment
?: angle made by the line joining center of dipole and the point with the dipole moment vector
r: distance between the center of dipole and the point
Note:
Approximation is made that the length of dipole is negligible as compared to the distance of the point from the dipole.