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 $$1.5 \times 10^{3}\ N/C$$ and points radially inward, what is the net charge on the sphere?

Answer 1

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

$$\displaystyle E=\frac{q}{4\pi\in_0d^2}$$

Where,

$$q =$$ Net charge = $$ 1.5 \times 10^3$$ N/C

$$d =$$ $$= 20 cm = 0.2 m$$

And, $$\displaystyle \frac{1}{4\pi\in_0}=9\times 10^9Nm^2C^{-2}$$

$$\therefore q=E(4\pi\in_0)d^2$$

$$\displaystyle =\frac{1.5\times 10^3\times (0.2)^2}{9\times 10^9}$$

$$=6.67 \times 10^9 C$$

$$=6.67 nC$$.

Because the electric field lines point radially inwards, the charge on the sphere is negative. Therefore, the net charge on the sphere is 6.67 nC.