# Q 1.21: A conducting sphere of radius 10 cm has an unknown charge. If the electric field 20 cm from the centre of the sphere is $1.5 \times 10^{3}\frac{N}{C}$ and points radially inward, what is the net charge on the sphere?

We know, for determining the electric field at r>R for a conducting sphere, the sphere can be considered as a point charge located at its centre.

Also, electric field intensity at a point P, located at a distance r, due to net charge q is given by,

$E = k\frac{q}{r^2}$

Given, r = 20 cm = 0.2 m  (From the centre, not from the surface!)

$\\ \therefore 1.5\times10^3 = 9\times10^9\times \frac{q}{0.2^2} \\ \implies q = \frac{1.5\times0.04}{9}\times10^{-6} = 6.67\times10^{-9}\ C$

Therefore, Charge on the conducting sphere is $- 6.67\ nC$ (Since flux is inwards)

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