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Answer the Following Question. Derive an Expression for the Electric Field at Any Point on the Equatorial Line of an Electric Dipole. - Physics

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Answer in Brief

Answer the following question.
Derive an expression for the electric field at any point on the equatorial line of an electric dipole. 

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Solution

Electric field for points on the equator plane 

The magnitude of the electric field due to two charges +q and –q is 

`E_(+q) = q/(4piε_0)1/(r^2 + a^2)`

`E_(-q) = q/(4piε_0)1/(r^2 + a^2)`

`E_(+q) = E_(-q)`

The directions of `E_(+q) and E_(-q)`, are as shown in the figure. The components normal to the dipole axis cancel away. The components along the dipole axis add up. 

Total electric field, `E = -(E_(+q) + E_(-q)) costheta  hatp` ......(Negative sign shows that the field is opposite to `hatp`)

`E = -(2qa)/(4piε_0(r^2 + a^2)^(3/2))hatp`       ...(iii)

At large distance (r >> a), this reduces to,

`E = -(2qa)/(4piε_0r^3)hatp`

`vecp = q xx 2vecahatp`

`E = -vecp/(4piε_0r^3)`    ....(r >> a)

Concept: Electric Dipole
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