Math, asked by avman08, 1 year ago

Derive an expression for electric potential at any point due to an electric dipole.​

Answers

Answered by Anonymous
10

Answer:

Therefore, the electric potential due to an electric dipole at a given point is equal to KPcosθr2−a2cos2θ. ... Therefore, V=KPcos(π2)r2−a2cos2(π2). We know cos(π2)=0. Hence, V=KPcos(π2)r2−a2cos2(π2)=KP(0)r2−a2 (0)

Step-by-step explanation:

@Genius

Answered by ferozpurwale
0

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)

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