Science (English Medium) Class 12 - CBSE Question Bank Solutions for Physics

Which of the following statements is not true about Gauss’s law?

Dielectric constant for a metal is ______.

When air is replaced by a dielectric medium of constant K, the maximum force of attraction between two charges separated by a distance ______.

Three capacitors 2µF, 3µF, and 6µF are joined in series with each other. The equivalent capacitance is ____________.

The Electric flux through the surface

(i)	(ii)
(iii)	(iv)

Five charges q₁, q₂, q₃, q₄, and q₅ are fixed at their positions as shown in figure. S is a Gaussian surface. The Gauss’s law is given by `oint_s E.ds = q/ε_0`

Which of the following statements is correct?

If `oint_s` E.dS = 0 over a surface, then ______.

1. the electric field inside the surface and on it is zero.
2. the electric field inside the surface is necessarily uniform.
3. the number of flux lines entering the surface must be equal to the number of flux lines leaving it.
4. all charges must necessarily be outside the surface.

If there were only one type of charge in the universe, then ______.

1. `oint_s` E.dS ≠ 0 on any surface.
2. `oint_s` E.dS = 0 if the charge is outside the surface.
3. `oint_s` E.dS could not be defined.
4. `oint_s` E.dS = `q/ε_0` if charges of magnitude q were inside the surface.

Consider a region inside which there are various types of charges but the total charge is zero. At points outside the region

1. the electric field is necessarily zero.
2. the electric field is due to the dipole moment of the charge distribution only.
3. the dominant electric field is `∞ 1/r^3`, for large r, where r is the distance from a origin in this region.
4. the work done to move a charged particle along a closed path, away from the region, will be zero.

Refer to the arrangement of charges in figure and a Gaussian surface of radius R with Q at the centre. Then

1. total flux through the surface of the sphere is `(-Q)/ε_0`.
2. field on the surface of the sphere is `(-Q)/(4 piε_0 R^2)`.
3. flux through the surface of sphere due to 5Q is zero.
4. field on the surface of sphere due to –2Q is same everywhere.

An arbitrary surface encloses a dipole. What is the electric flux through this surface?

If the total charge enclosed by a surface is zero, does it imply that the elecric field everywhere on the surface is zero? Conversely, if the electric field everywhere on a surface is zero, does it imply that net charge inside is zero.

In 1959 Lyttleton and Bondi suggested that the expansion of the Universe could be explained if matter carried a net charge. Suppose that the Universe is made up of hydrogen atoms with a number density N, which is maintained a constant. Let the charge on the proton be: e_p = – (1 + y)e where e is the electronic charge.

1. Find the critical value of y such that expansion may start.
2. Show that the velocity of expansion is proportional to the distance from the centre.

A capacitor of 4 µ F is connected as shown in the circuit (Figure). The internal resistance of the battery is 0.5 Ω. The amount of charge on the capacitor plates will be ______.

Consider two conducting spheres of radii R₁ and R₂ with R₁ > R₂. If the two are at the same potential, the larger sphere has more charge than the smaller sphere. State whether the charge density of the smaller sphere is more or less than that of the larger one.

Can the potential function have a maximum or minimum in free space?

A parallel plate capacitor is filled by a dielectric whose relative permittivity varies with the applied voltage (U) as ε = αU where α = 2V^–1. A similar capacitor with no dielectric is charged to U₀ = 78V. It is then connected to the uncharged capacitor with the dielectric. Find the final voltage on the capacitors.

A parallel plate capacitor (A) of capacitance C is charged by a battery to voltage V. The battery is disconnected and an uncharged capacitor (B) of capacitance 2C is connected across A. Find the ratio of final charges on A and B.

Read the following paragraph and answer the questions.

1. Find the equivalent capacitance between points A and B in the given diagram.
   
2. A dielectric slab is inserted between the plates of the parallel plate capacitor. The electric field between the plates decreases. Explain.
3. A capacitor A of capacitance C, having charge Q is connected across another uncharged capacitor B of capacitance 2C. Find an expression for (a) the potential difference across the combination and (b) the charge lost by capacitor A.
   OR
   Two slabs of dielectric constants 2K and K fill the space between the plates of a parallel plate capacitor of plate area A and plate separation d as shown in the figure. Find an expression for the capacitance of the system.
    

A charge Q is placed at the centre of a cube. The electric flux through one of its faces is ______.