Electric flux through a hemisphere

JEE Advanced 2017 Paper 2, Question 10

A point charge +Q is placed just outside an imaginary hemispherical surface of radius {\rm R} as shown in the figure. Which of the following statements is/are correct?

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  1. The electric flux passing through the curved surface of the hemisphere is -\frac{Q}{2 \varepsilon_{0}}\left(1-\frac{1}{\sqrt{2}}\right)
  2. Total flux through the curved and the flat surfaces is \frac{Q}{\varepsilon_{0}}
  3. The component of the electric field normal to the flat surface is constant over the surface
  4. The circumference of the flat surface is an equipotential

Related Problems:
Flux from a charged shell
Conducting wire in a magnetic field

Solution

In problems like these a beginner may …

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A spherical capacitor

A spherical conducting shell with radius b is concentric with a conducting ball with radius a, with a<b.

  1. Compute the capacitance C = Q / \Delta \phi when the shell is grounded and the ball has charge Q.
  2. Compute the capacitance when the ball is grounded and the shell has charge Q.
  3. Compute the full matrix of coefficients of capacitance for the two conductors.
  4. Considering these conductors as a capacitor, determine its capacitance. That is, assign equal and opposite charges \pm Q to the shell and the ball, and compute C = Q / \Delta \phi.

Related Problem: Insulating spherical shell with a hole

Solution

(a) First, we ground the shell and give the …

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Electric field in a hollow region

IIT-JEE 2007 Paper 2, Question 6

(This problem is was repeated in JEE Advanced 2015 Paper 2, Question 11)

A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is

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  1. zero everywhere
  2. non-zero and uniform
  3. non-uniform
  4. zero only at its center

Related Problems:
Electric field from a sphere with a cavity
Flux from a charged shell
Charge at one corner of a cube

Solution

As explained in a related problem we can think of the given charge distribution as a …

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Charge at one corner of a cube

A charge q sits at one corner of a cube of side length a as shown in the figure below. What is the electric flux through the shaded side?

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Related problems:
Electric field from a sphere with a cavity
Electric field in a hollow region
Flux from a charged shell

Solution

Since the problem is asking us to find the electric flux it is natural to guess that we need to apply Gauss’s Law. However, we need a closed surface with appropriate symmetry to be able to use Gauss’s Law (see article). So we consider the situation shown below.

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We have placed …

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Electric field from a sphere with a cavity

A sphere of radius a is filled with positive charge with uniform density \rho. Then a smaller sphere of radius a/2 is carved out, as shown in the figure below, and left empty. What are the direction and magnitude of the electric field at A? At B?

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Related problems:
Electric field in a hollow region
Charge at one corner of a cube
Flux from a charged shell

Solution

This problem can be solved by using the principle of superposition. For instance, consider a point charge +q at some point P in space. It creates an electric field everywhere. However, if you place a …

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