PYQ NEET- Electric Charges And Fields L-2

Question: A spherical conductor of radius 10 $\mathrm{cm}$ has a charge of $3.2 \times 10^{-7} \mathrm{C}$ distributed uniformly. What is the magnitude of electric field at a point $15 \mathrm{~cm}$ from the centre of the sphere?#

$$ \left(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \mathrm{Nm}^2 / \mathrm{C}^2\right) $$

A) $1.28 \times 10^5 \mathrm{~N} / \mathrm{C}$

B) $1.28 \times 10^6 \mathrm{~N} / \mathrm{C}$

C) $1.28 \times 10^7 \mathrm{~N} / \mathrm{C}$

D) $1.28 \times 10^4 \mathrm{~N} / \mathrm{C}$

Answer: $1.28 \times 10^5 \mathrm{~N} / \mathrm{C}$#

Sol:#

Given, radius, $r=10 \mathrm{~cm}=10 \times 10^{-2} \mathrm{~m}$ Charge, $q=3.2 \times 10^{-7} \mathrm{C}$ Electric field, $E=$ ? Electric field at a point $(x=15 \mathrm{~cm})$ from the centre of the sphere is $$ \begin{aligned} E & =\frac{1}{4 \pi \varepsilon_0} \cdot \frac{q}{x^2} \ & =9 \times 10^9 \times \frac{3.2 \times 10^{-7}}{\left(15 \times 10^{-2}\right)^2} \ & =1.28 \times 10^5 \mathrm{~N} / \mathrm{C} \end{aligned} $$

Hence, correct option is (a).