Physics, asked by mohitmeenaji00, 3 months ago

define electric potential, obtain an expression of electric potential due to an electric dipole at any point (r,o) draws necessary diagram​

Answers

Answered by saleha55510
4

Answer:

Let an electric dipole consist of two equal and opposite point charges –q at A and +q at B ,separated by a small distance AB =2a ,with centre at O.

The dipole moment, p=q×2a

We will calculate potential at any point P, where

OP=r and ∠BOP=θ

Let BP=r

1

and AP=r

2

Draw AC perpendicular PQ and BD perpendicular PO

In ΔAOC cosθ=OC/OA=OC/a

OC=acosθ

Similarly, OD=acosθ

Potential at P due to +q=

4πϵ

0

1

r

2

q

And Potential at P due to −q=

4πϵ

0

1

r

1

q

Net potential at P due to the dipole

V=

4πϵ

0

1

(

r

2

q

r

1

q

)

⟹V=

4πϵ

0

q

(

r

2

1

r

1

1

)

Now, r

1

=AP=CP

=OP+OC

=r+acosθ

And r

2

=BP=DP

=OP–OD

=r−acosθ

V=

4πϵ

0

q

(

r−acosθ

1

r+acosθ

1

)

=

4πϵ

0

q

(

r

2

−a

2

cos

2

θ

2acosθ

)

=

r

2

−a

2

cos

2

θ

pcosθ

(Since p=2aq)

Special cases:-

(i) When the point P lies on the axial line of the dipole, θ=0

cosθ=1

V=

r

2

−a

2

p

If a<<r, V=

r

2

p

Thus due to an electric dipole ,potential, V∝

r

2

1

(ii) When the point P lies on the equatorial line of the dipole, θ=90

cosθ=0

i.e electric potential due to an electric dipole is zero at every point on the equatorial line of the dipole

Similar questions