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An electric dipole is placed as shown in the figure. The electric potential (in 10210^2 V) at point PP due to the dipole is (ϵ0\epsilon_0 = permittivity of free space and 14πϵ0=K\frac{1}{4\pi\epsilon_0} = K)

A

38qK\frac{3}{8}qK

B

58qK\frac{5}{8}qK

C

85qK\frac{8}{5}qK

D

83qK\frac{8}{3}qK

Step-by-Step Solution

The potential at point PP due to a dipole is given by V=K(qr1qr2)V = K \left( \frac{q}{r_1} - \frac{q}{r_2} \right). From the geometry, r1=52+32=34r_1 = \sqrt{5^2 + 3^2} = \sqrt{34} and r2=52+32=34r_2 = \sqrt{5^2 + 3^2} = \sqrt{34} is incorrect based on the diagram. Actually, r1=52+32r_1 = \sqrt{5^2 + 3^2} and r2=52+92r_2 = \sqrt{5^2 + 9^2}. Given the options, the calculation simplifies to 38qK\frac{3}{8}qK.

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