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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?

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#### 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_0"d"^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.

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