#### 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 × 10^{3 }N/C and points radially inward, what is the net charge on the sphere?

#### Solution

Electric field intensity (*E*) at a distance (*d*) from the centre of a sphere containing net charge *q* is given by the relation,

`E=q/(4piin_0d^2)`

Where,

*q* = Net charge = 1.5 × 10^{3} N/C

*d *= Distance from the centre = 20 cm = 0.2 m

∈_{0} = Permittivity of free space

And,`1/(4piin_0)` = 9 × 10^{9} N m^{2} C^{−2}

∴`q=E(4piin_0)d^2`

`=(1.5xx10^3xx(0.2)^2)/(9xx10^9)`

= 6.67 × 10^{9} C

= 6.67 nC

Therefore, the net charge on the sphere is 6.67 nC.

Is there an error in this question or solution?

Solution 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 × 10^3 N/C and points radially inward, what is the net charge on the sphere? Concept: Electric Charges.