A small charged particle ‘q’ lies at the centre of two concentric conducting hollow spheres of inner radii R and 5R and outer radii 3R and 7R respectively. Then which of the following is/are correct.

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The energy stored in the space between 3R to 5R (cavity) is $\frac{k q^{2}}{15 R}$ .

The amount of work has to be performed to slowly transfer the charge ‘q’ from center through the orifice to infinity is $\frac{29}{210} \frac{k q^{2}}{R}$ .

The amount of work has to be performed to slowly transfer the charge ‘q’ from center through the orifice to infinity is $\frac{38}{105} \frac{k q^{2}}{R}$ .

The energy stored in the space between 3R to 5R (cavity) is $\frac{k q^{2}}{30 R}$ .

answer is A, D.

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Detailed Solution

Work performed = $\int_{R}^{3 R} \frac{1}{2} ε_{0} E^{2} d V + \int_{5 R}^{7 R} \frac{1}{2} ε_{0} E^{2} d V = \frac{k q^{2}}{3 R} + \frac{k q^{2}}{35 R}$