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Question #42845

Difficulty: 8/10 | 🟢 Free

The Question

A fixed infinite non-conducting flat sheet lies in the $y-z$ plane ( $x=0$ ) and has a uniform surface charge density $+\sigma$ and a uniform surface mass density $\mu$ . A fixed thin non-conducting spherical shell of radius $R$ , total mass $M$ , and total charge $+Q$ (uniformly distributed) is centered at the coordinates $(4R, 0, 0)$ . A point particle of mass $m$ and charge $+q$ is released from rest at the coordinates $(4.5R, 0, 0)$ . What is the magnitude of the initial acceleration of the particle? (Given: $G$ is the universal gravitational constant, $\varepsilon_0$ is the permittivity of free space)

Options

A.
$\left| \frac{q\sigma}{2m\varepsilon_0} - 2\pi G \mu \right|$
B.
$0$
C.
$\left| \frac{q\sigma}{2m\varepsilon_0} - 2\pi G \mu + \frac{qQ}{\pi m \varepsilon_0 R^2} - \frac{4GM}{R^2} \right|$
D.
$\left| \frac{q\sigma}{2m\varepsilon_0} - 4\pi G \mu \right|$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Field due to Infinite Sheet|Shell Theorem (Internal vs External)|Superposition of Potentials

Why This Question Is Tricky

Common Mistakes

This question tests the student's robust understanding of the Principle of Superposition and the Shell Theorem.

A common critical error is assuming that the interior of a shell is a 'zero-field' region universally, effectively treating the non-conducting shell as a shield against external fields (a misapplied Faraday cage concept, which also would not shield gravity).

Students falling for this trap will incorrectly choose zero acceleration.

Another prevalent mistake is ignoring the Shell Theorem entirely and treating the shell as a point mass/charge at its center, leading to the inclusion of non-existent internal forces.

The problem forces the realization that while the shell's self-contribution to the interior field is zero, external fields from the infinite sheet permeate the space unaltered.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Electric Charges and Fields - Class 12
Concept	Field due to Infinite Sheet
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free