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Physics Question on Electric Charge

A conducting sphere of radius 10 cm10\,cm has unknown charge. If the electric field at a distance 20 cm20\,cm from the centre of the sphere is 1.2×103 N C−11.2 \times 10^3\, N\, C^{-1} and points radially inwards. The net charge on the sphere is

A

−4.5×10−9 C-4.5 \times 10^{-9}\, C

B

4.5×109 C4.5 \times 10^{9}\, C

C

−5.3×10−9 C-5.3 \times 10^{-9}\, C

D

5.3×109 C5.3 \times 10^{9}\, C

Answer

−5.3×10−9 C-5.3 \times 10^{-9}\, C

Explanation

Solution

Here, distance of point from the centre of the sphere, r=20 cm=0.2 mr = 20 \,cm = 0.2 \,m Electric field, E=−1.2×103 N C−1E = -1.2 \times 10^3\,N\, C^{-1} As E=q4πε0r2E=\frac{q}{4\pi\varepsilon_{0}r^{2}} ∴q=(4πε0r2)E=(0.2)2×(−1.2×103)9×109\therefore q=\left(4\pi\varepsilon_{0}r^{2}\right)E=\frac{\left(0.2\right)^{2}\times\left(-1.2\times10^{3}\right)}{9\times10^{9}} =−5.3×10−9 C=-5.3\times10^{-9}\,C