At distance of 5cm and 10cm outwards from the surface of a uniformly changed non conducting solid sphere, the potentials are 100V and 75V respectively. Then

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The electric potential at its centre is 225 V

The potential at the surface of the sphere is 150V

The electric field on the surface of the sphere is 1500 V/m

The charge on the sphere is $\frac{5}{3} \times 10^{- 9} C$

answer is A, B, C, D.

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Detailed Solution

Let 'r' be the radius of the surface of sphere.

$\frac{k q}{r + 5} = 100$

$\frac{k q}{r + 10} = 75$

$\Rightarrow r = 10 c m, k q = 15$

$\Rightarrow q \times 9 \times 10^{9} = 15 \Rightarrow q = \frac{5}{3} \times 10^{- 9} C$

$E_{s} = \frac{q}{4 π ε_{0} \times {(0.1)}^{2}} = \frac{5}{3} \times 10^{- 9} \times 9 \times 10^{9} \times 10^{2} = 1500 V / m$

$V_{s} = \frac{k q}{r} = 150 V$

$V_{c} = \frac{3}{2} V_{s} = \frac{3}{2} \times 150 = 225 V$

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