Continuous Charge Distribution

IMPORTANT

Continuous Charge Distribution: Overview

This topic covers concepts such as Continuous Charge Distribution, Line Charge Distribution, Surface Charge Distribution, and Volume Charge Distribution.

Important Questions on Continuous Charge Distribution

MEDIUM
IMPORTANT

A spherical conducting shell of inner radius  r 1 and outer radius r2 has a charge Q. A charge q is placed at the centre of the shell.
What is the surface charge density on the (i) inner surface, (ii) outer surface of the shell?

EASY
IMPORTANT

Describe linear charge density. Write its SI unit.

EASY
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What is volume charge density? Write its SI unit.

EASY
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Describe linear charge density.

EASY
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What is volume charge distribution?

EASY
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Explain the term volume charge density. Write its SI unit.

EASY
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Explain the term surface charge density. Write its Sl unit.

EASY
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Find the total charge on a thin disc of radius R, if its surface charge density varies with distance r from centre as σ=σ0Rr

HARD
IMPORTANT

A straight infinitely long cylinder of radius R0=10cm is uniformly charged with a surface charge density σ=+1012C/m2. The cylinder serves as a source of electrons, with the velocity of the emitted electrons perpendicular to its surface. Electron velocity must be ×105m/s to ensure that electrons can move away, from the axis of the cylinder to a distance greater than r=103m.

HARD
IMPORTANT

A solid sphere of radius R has a charge Q distributed in its volume with a charge density ρ=κra, where κ and a are constants and r is the distance from its centre. If the electric field at r=R2 is 18 times that at r=R, find the value of a.

MEDIUM
IMPORTANT

Two metal spheres, one of radius R and the other of radius 2R , both have same surface charge density σ . If they are brought in contact and separated, then the new surface charge density on each of the sphere are respectively

HARD
IMPORTANT

Find the force experienced by the semicircular rod charged with a charge q, placed as shown in figure. Radius of the wire is R and the infinite line of charge with linear charge density is passing through its centre and perpendicular to the plane of rod.
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EASY
IMPORTANT

A small element l is cut from a circular ring of radius α and λ charge per unit length. The net electric field at the centre of ring is

HARD
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Two infinitely long line charge of same linear charge density λ are arranged as shown in figure. The magnitude of electric field intensity at point P as shown in figure -


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HARD
IMPORTANT

An infinite long line charge of charge per unit length λ is passing one of the edge of a cube. Length of edge of the cube is l. (see figure)

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HARD
IMPORTANT

The figure shows two large, closely placed, parallel, nonconducting sheets with identical (positive) uniform surface charge densities, and a sphere with a uniform (positive) volume charge density. Four points marked as 1, 2, 3 and 4 are shown in the space in between. If E1, E2, E3 and E4 are magnitude of net electric fields at these points respectively then:

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HARD
IMPORTANT

A solid sphere of radius R1 and volume charge density ρ=ρ0r is enclosed by a hollow sphere of radius R2 with negative surface charge density σ , such that the total charge in the system is zero, ρ0 is a positive constant and r is the distance from the centre of the sphere. The ratio R2R1 is 

HARD
IMPORTANT

Charge distribution of a solid sphere, having radius R1 and volume charge density, ρ=ρ0r, is enclosed by a hollow sphere of radius R2 with negative surface charge density σ such that the total charge in the system is zero. ρ0 is a positive constant and r is the distance from the centre of the sphere. The ratio R2R1 is,

MEDIUM
IMPORTANT

When a charge of amount Q is given to an isolated metal plate X of surface area A, its surface charge density becomes σ1. When an isolated identical plate Y is brought closer to X, the surface charge density on X becomes σ2. When Y is earthed, the surface charge density becomes σ3. Then -

HARD
IMPORTANT

Two mutually perpendicular infinitely long lines of charge having charge per unit length as λ1 and λ2 are located in air at a distance a from each other. The force of interaction between them is