SATHEE: Electrostatic Potential and Capacitance

Electrostatic Potential and Capacitance - Result Question 20

22. Each corner of a cube of side $l$ has a negative charge, $- q$ . The electrostatic potential energy of a charge $q$ at the centre of the cube is [2002]

(a) $- \frac{4 q^{2}}{\sqrt{2} π ε_{0} l}$

(b) $\frac{\sqrt{3} q^{2}}{4 π ε_{0} l}$

(d) $- \frac{4 q^{2}}{\sqrt{3} π ε_{0} l}$

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Answer:

Correct Answer: 22. (d)

Solution:

(d) Length of body diagonal $= \sqrt{3} ℓ$

$∴$ Distance of centre of cube from each corner

$r = \frac{\sqrt{3}}{2} ℓ$

P.E. at centre

$= 8 \times$ Potential Energy of the charge $(+ q)$ due to charge $(- q)$ at one corner

$= 8 \times \frac{K q \times (- q)}{r}$

$= 8 \times \frac{1}{4 π ε_{0} \sqrt{3} l} \times 2 \times q \times (- q) = \frac{- 4 q^{2}}{\sqrt{3} π ε_{0} l}$

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Electrostatic Potential and Capacitance - Result Question 20

22. Each corner of a cube of side l has a negative charge, −q. The electrostatic potential energy of a charge q at the centre of the cube is [2002]

Answer:

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22. Each corner of a cube of side $l$ has a negative charge, $- q$ . The electrostatic potential energy of a charge $q$ at the centre of the cube is [2002]