2020 Electric Charges and FieldsGauss's Law – Field due to a Charged Conducting Sphere Medium Question 12 of 42 in Electric Charges and Fields

A spherical conductor of radius 10 cm has a charge of $3.2\times10^{-7}\ C$ distributed uniformly. What is the magnitude of electric field at a point 15 cm from the centre of the sphere? ($\frac{1}{4\pi\epsilon_0}=9\times10^9\ N\,m^2/C^2$)

A $1.28\times10^5\ N/C$
B $1.28\times10^6\ N/C$
C $1.28\times10^7\ N/C$
D $1.28\times10^4\ N/C$

The answer is A.

Solution

Outside a charged conducting sphere, the field is as if the whole charge were at the centre: $E = \frac{1}{4\pi\epsilon_0}\frac{Q}{r^2} = \frac{9 \times 10^9 \times 3.2 \times 10^{-7}}{(15 \times 10^{-2})^2} = \frac{2880}{225 \times 10^{-4}}$ $= 1.28 \times 10^5$ N/C

Concept field outside a charged sphere

Electric Charges and Fields in past papers

42 questions from this chapter have appeared across 23 exam years.