Question

ind 2019-20 SF
(b) Find the SI unit of permittivity (Ev) of free space.
(c) Write down the expression of potential for a dipole with moment P.​

Answer 1

Answer:

Hii,

Explanation:

b)The standard SI unit for permittivity is farad per meter (F/m or F·m−1).

c)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 01r 2q

And Potential at P due to −q= 4πϵ 01r 1q

Net potential at P due to the dipole

V= 4πϵ 01

( r 2q − r 1q )

⟹V= 4πϵ 0q

( r 21− r 11 )

Now, r 1

=AP=CP

=OP+OC

=r+acosθ

And r 2

=BP=DP

=OP–OD

=r−acosθ

V= 4πϵ 0q

( r−acosθ 1 − r+acos θ 1)

= 4πϵ 0q

( r 2 −a 2 cos 2θ2acosθ )

= r 2−a 2cos 2θpcosθ

(Since p=2aq)