CBSE Class 12 Physics 2019 Delhi Set 1 Paper

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Question : 13
Total: 27
SECTION -C

(a) Draw the equipotential surfaces corresponding to a uniform electric field in the Z-direction.
(b) Derive an expression for the electric potential at any point along the axial line of an electric dipole.
Solution:  
(a)Drawing of equipotential surfaces
(b) Derivation of the expression of electric potential

(b)

Potential at point P
‌Vp=V−q+V+q
‌=‌
1
4πε0
‌
−q
(r+a)
+‌
1
4πε0
‌
q
(r−a)

‌=‌
q
4πε0
[‌
1
(r−a)
−‌
1
(r+a)
]

‌=‌
q
4πε0
[‌
r+a−r+a
(r−a)(r+a)
]

‌=‌
q
4πε0
×
‌
2a
(r2−a2)
=‌
q×2a
4πε0(r2−a2)

‌=‌
1
4πε0
‌
p
(r2−a2)

where, p is the dipole moment.
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