Electric Charges and Fields - Result Question 12
12. A spherical conductor of radius $10 cm$ has a charge of $3.2 \times 10^{-7} C$ distributed uniformly. What is the magnitude of electric field at a point $15 cm$ from the centre of the sphere? [2020] $(\frac{1}{4 \pi \epsilon_0}=9 \times 10^{9} Nm^{2} / C^{2})$
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======= ####12. A spherical conductor of radius $10 cm$ has a charge of $3.2 \times 10^{-7} C$ distributed uniformly. What is the magnitude of electric field at a point $15 cm$ from the centre of the sphere? [2020] $(\frac{1}{4 \pi \epsilon_0}=9 \times 10^{9} Nm^{2} / C^{2})$
c3eec34ec6b1fad69db54a20ad4b2dca40c2aa54 (a) $1.28 \times 10^{5} N / C$
(b) $1.28 \times 10^{6} N / C$
(c) $1.28 \times 10^{7} N / C$
(d) $1.28 \times 10^{4} N / C$
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Answer:
Correct Answer: 12. (a)
Solution:
- (a) If the charge on a spherical conductor of radius $R$ is $Q$, then electric field at distance $r$ from centre is
$ \begin{matrix} E=0 & (\text{ if } r \angle R) \\ E=\frac{1}{4 \pi \epsilon_0} \frac{Q}{r^{2}} & (\text{ if } r \geq R) \end{matrix} $
Electric field at a distance $15 cm$ from the centre of sphere will be
$ \begin{aligned} & E=\frac{9 \times 10^{9} \times 3.2 \times 10^{-7}}{225 \times 10^{-4}} \\ & =0.128 \times 10^{6}=1.28 \times 10^{5} N / C \end{aligned} $
