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QPages 141-142: Q11: HC Verma: Concepts of Physics - Volume 2 Gauss's Law Pages 141-142: Q11 Solution: A charge Q is distributed uniformly within the material of a…

A charge Q is distributed uniformly within the material of a hollow sphere of inner and outer radii

r_1

and

r_2

see the figure). Find the electric field at a point P at a distance x away from the centre for

r_1 < x < r_2

. Draw a rough graph showing the electric field as a function of x for

0 < x < 2r_2

see the figure).

Step-by-Step Verified Solution

**Answer:**

E = \frac{Q(x^3 - r_1^3)}{4\pi\epsilon_0 x^2(r_2^3 - r_1^3)}

. **Step-by-Step Explanation:** For a point inside the shell material (

r_1 < x < r_2

): Charge enclosed:

Q_{enc} = Q \times \frac{x^3 - r_1^3}{r_2^3 - r_1^3}

. By Gauss's law:

E \times 4\pi x^2 = \frac{Q_{enc}}{\epsilon_0}

.

E = \frac{Q(x^3 - r_1^3)}{4\pi\epsilon_0 x^2(r_2^3 - r_1^3)}

Graph: E = 0 for x < r_, increases to a maximum, then decreases as 1/x_ for x > r_ .

All Questions in this Chapter

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