Before You Begin

Question #42483

Difficulty: 8/10 | 🟢 Free

The Question

A solid non-conducting sphere of radius $R$ has a uniform volume charge density. A spherical cavity of radius $R/2$ is created such that its surface touches the center of the original sphere and its outer surface. The total charge of the remaining object is $Q$ . A point charge $q$ (of the same sign as $Q$ ) is projected from infinity along the axis passing through the centers of the original sphere and the cavity, such that it enters the object through the cavity. What is the minimum initial kinetic energy $K_0$ required for the point charge to reach the center of the original sphere? (Assume the electrostatic potential at infinity is zero, and $k = \frac{1}{4\pi\epsilon_0}$ ).

Options

A.
$\frac{10kQq}{7R}$
B.
$\frac{5kQq}{4R}$
C.
$\frac{8kQq}{7R}$
D.
$\frac{6kQq}{7R}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Multi-Concept_Bridge

Master problems that require linking physics and math concepts to solve complex competitive questions.

Concepts Behind This Question

Potential Energy Reference|Non-conducting Charged Sphere|Integration

Why This Question Is Tricky

Common Mistakes

This question tests the rigorous application of the principle of superposition for electrostatic potential in non-conducting charge distributions with cavities.

The primary trap is assuming the given charge $Q$ is the charge of the original uncut sphere rather than the remaining object, which leads to the incorrect option B.

A secondary trap involves incorrectly calculating the potential of the removed cavity at the origin by treating it as a point charge at its center, rather than recognizing the origin lies exactly on the surface of the cavity.

Furthermore, it verifies if the student understands that the uniform non-zero field inside the cavity implies the potential is not constant, making the origin the true point of maximum potential along the path.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Work, Energy, and Power - Class 11 Part 1
Concept	Potential Energy Reference
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free