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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?


Solution

$$\textbf{Step 1: Electric field outside a conducting sphere}$$
                 $$E = \dfrac{1}{4\pi \in_0} \dfrac{q}{r^2}$$
where $$r$$ is the distance from the centre of conducting sphere.

                 $$\therefore q = 4\pi \in_0 E \ r^2$$           $$....(1)$$

$$\textbf{Step 2: Substituting the values }$$

                  $$q = \dfrac{1}{9\times 10^9} \times 1.5 \times 10^3N/C \times (0.2m)^2$$$$= 6.67\times 10^{-9}C = 6.67nC$$
Because the electric field lines point radially inwards, the nature of the charge on the sphere is negative.
Therefore $$q=-6.67 nC$$


Physics
NCERT
Standard XII

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