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Q.

A spherical conductor of radius 10 cm has a charge of 3.2 x 10^-7 C distributed uniforrmly. What is the magnitude of electric field at a point 15 cm from the centre of the sphere? $(\frac{1}{4 π ε_{0}} = 9 \times 10^{9} N - m^{2} / C^{2})$

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a

1.28 $\times$ 10⁵ N/C

b

1.28 $\times$ 10⁴ N/C

c

1.28 $\times$ 10⁷ N/C

d

1.28 $\times$ 10⁶ N/C

answer is A.

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Detailed Solution

Given, radius, $r = 10 cm = 10 \times 10^{- 2} m$

$Charge, q = 3.2 \times 10^{- 7} C$

Electric field, E = ?

Electric field at a point (x = 15 cm) from the centre of the sphere is

$E = \frac{1}{4 π ε_{0}} \cdot \frac{q}{x^{2}} = 9 \times 10^{9} \times \frac{3.2 \times 10^{- 7}}{{(15 \times 10^{- 2})}^{2}}$

$= 1.28 \times 10^{5} N / C$

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