Question:

A conducting sphere of radius 10 cm has an unknown charge. If the electric field 20 cm from the centre of the sphere is 1.5×103NC11.5 × 10^3 NC^{-1} and points radially inward, what is the net charge on the sphere?

Updated On: Sep 28, 2023
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Solution and Explanation

Electric field intensity (E) at a distance (d) from the centre of a sphere containing net charge q is given by the relation, 
E=14πε0.qd2E = \frac{1 }{ 4πε_0}.\frac {q}{d^2}
Where, q=q = Net charge = 1.5×103NC11.5 × 10^3 NC^{-1}
d=d = Distance from the centre =20cm=0.2m= 20 cm = 0.2 m
ε0ε_0 =  Permittivity of free space and  14 πε0\frac{ 1 }{ 4 πε_0} = 9 ×109Nm2C29 × 10^9 Nm^2C^{-2}
Therefore, 
             q=E(4πε0)d2=1.5 ×1039 ×109q = E(4πε_0)d^2 = \frac{1.5 × 10^3 }{9 × 10^9}
=6.67×109C= 6.67 × 10^9\,C
=6.67nC= 6.67 nC
Therefore, the net charge on the sphere is 6.67 nC.

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