SATHEE: Electrostatics Question 734

Electrostatics Question 734

Question: A solid sphere of radius R has a charge Q distributed in its volume with a charge density $ρ = k r^{a}$ , where k and an are constants and r is the distance from its center. If the electric field at $r = \frac{R}{2}$ is $\frac{1}{8}$ times that at $r = R$ , the value of a is.

Options:

A) 3

B) 5

C) 2

D) both [a] and [b]

Show Answer

Answer:

Correct Answer: C

Solution:

[c] Using Gauss’s law, we have $\int_{\vec{E} . d \vec{A}} = \frac{1}{\in_{0}} \int_{}^{} (ρ d v) = \frac{1}{\in_{0}} \int_{0}^{R} k r^{a} \times 4 π r^{2} d r$

$or E \times 4 π r^{2} = (\frac{4 π k}{\in_{0}}) \frac{R^{(a + 3)}}{(a + 3)}$

$∴ E_{1} = \frac{k R^{(a + 1)}}{\in_{0} (a + 3)}$

$For r = \frac{R}{2} \cdot E_{2}$

= $\frac{k {(\frac{R}{2})}^{a + 1}}{\in_{0}} (a + 3) = \frac{1}{8} \frac{k R^{(a + 1)}}{\in_{0} (a + 3)}$

$∴ 2^{\frac{1}{a + 1}} = \frac{1}{8} or a = 2.$

Electrostatics Question 734

Question: A solid sphere of radius R has a charge Q distributed in its volume with a charge density $ρ = k r^{a}$ , where k and an are constants and r is the distance from its center. If the electric field at $r = \frac{R}{2}$ is $\frac{1}{8}$ times that at $r = R$ , the value of a is.

Options:

Answer:

Solution:

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Electrostatics Question 734

Question: A solid sphere of radius R has a charge Q distributed in its volume with a charge densityρ=kra , where k and an are constants and r is the distance from its center. If the electric field at r=R2 is 18 times that at r=R , the value of a is.

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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Question: A solid sphere of radius R has a charge Q distributed in its volume with a charge density $ρ = k r^{a}$ , where k and an are constants and r is the distance from its center. If the electric field at $r = \frac{R}{2}$ is $\frac{1}{8}$ times that at $r = R$ , the value of a is.