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QUESTION: 1

Two concentric sphere of radii * R* and

Solution:

By superposition Principle.

Electric Potential at common centre is

QUESTION: 2

A long string with a charge of λ per unit length passes through an imaginary cube of edge * l*. The maximum possible flux of electric field through the cube will be

Solution:

Maximum length of string =

Maximum enclosed charge =

The correct answer is:

QUESTION: 3

Force of attraction between the plate of a parallel plate capacitor is

Solution:

QUESTION: 4

Consider two concentric conducting spherical shell with inner and outer radii **a****, b, c** and

Solution:

For ** r < a**, applying Gauss’s law.

∴ *q* = 0

Also since shells are conducting

For ** b < r < c ** by Gauss’s law

For ** r > d**, applying Gauss’s law, we get

QUESTION: 5

Electric field in the region is given by Here, α is a constant of proper dimensions. The total flux passing through a cube bounded by the surfaces x = l , x = 2l, y = 0, y = l, z = 0, z = l.

Solution:

Except the faces *ABCD* and *EFGH*, for all the faces as

So, flux through the cube

The correct answer is: αl^{3}

QUESTION: 6

A spherical condenser has inner and outer sphere of radii * a * and

Solution:

Capacity of spherical condenser when outer sphere is earthed

Capacity of spherical condenser when inner sphere is earthed Difference in their capacity

The correct answer is:

QUESTION: 7

A diagram of an irregularly shaped charged conductor is shown at the right figure. Four location along the surface are labeled ** A, B, C, D**. Rank these locations in increasing order of the strength of their electric field beginning with the smallest electric field.

Solution:

For conducting surface, electric field are strongest at the location where the curvature is the greatest. *A* projection (such as at point *A*) is the extreme case of high carvature. *A* flat section of a surface (such as point *B*) is on the opposite extreme with the no curvature. So, point *B* is listed first and point *A* is listed last. Since point *D* is on a section of the surface which curve more than point *C*. The field at point *C* is more than field at point *B*.

The correct answer is: *B* < *C* < *D* < *A*

QUESTION: 8

A positively charge non-conducting disc having uniform surface change density α *coulomb/m*^{2}. The difference in the potential at its centre and at its edge is given by.

Solution:

Potential at the centre of disc. By taking a element of charge in the form of ring of radius *r* and thickness *dr*.

Now difference between the potential at the centre and at its edge is given by

*V* = *V*_{1} – *V*_{2}

QUESTION: 9

A metallic sphere of radius *r* and carrying a charge *q* is enclosed by a dielectric shell of thickness δ outer radius *r*_{2} and relative permittivity ε The medium elsewhere is air. The potential *V*(*r*) for *r* > *r*_{2} is

Solution:

*E* = *P* = *D* = 0 [Inside the metal sphere]

QUESTION: 10

A charged ball *B* hangs from a silk thread *S*, which make an angle θ and a large conducting sheet *P* as shown in the figure. The surface charge density σ of the sheet is proportional to

Solution:

For equilibrium

Dividing, we get

The correct answer is: tan θ

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