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

The emf induced across the ends of a conductor due to its motion in a magnetic field is called motional emf. It is produced due to magnetic Lorentz force acting on the free electrons of the conductor. For a circuit shown in the figure, if a conductor of length l moves with velocity v in a magnetic field B perpendicular to both its length and the direction of the magnetic field, then all the induced parameters are possible in the circuit.

A 0.1 m long conductor carrying a current of 50 A is held perpendicular to a magnetic field of 1.25 mT. The mechanical power required to move the conductor with a speed of 1 ms^-1 is ______.

The emf induced across the ends of a conductor due to its motion in a magnetic field is called motional emf. It is produced due to magnetic Lorentz force acting on the free electrons of the conductor. For a circuit shown in the figure, if a conductor of length l moves with velocity v in a magnetic field B perpendicular to both its length and the direction of the magnetic field, then all the induced parameters are possible in the circuit.

A bicycle generator creates 1.5 V at 15 km/hr. The EMF generated at 10 km/hr is ______.

Consider two different hydrogen atoms. The electron in each atom is in an excited state. Is it possible for the electrons to have different energies but same orbital angular momentum according to the Bohr model? Justify your answer.

Derive an expression for the frequency of radiation emitted when a hydrogen atom de-excites from level n to level (n – 1). Also show that for large values of n, this frequency equals to classical frequency of revolution of an electron.

Consider a uniform electric field in the ẑ direction. The potential is a constant ______.

1. in all space.
2. for any x for a given z.
3. for any y for a given z.
4. on the x-y plane for a given z.

Equipotential surfaces ______.

1. are closer in regions of large electric fields compared to regions of lower electric fields.
2. will be more crowded near sharp edges of a conductor.
3. will be more crowded near regions of large charge densities.
4. will always be equally spaced.

The work done to move a charge along an equipotential from A to B ______.

1. cannot be defined as `- int_A^B E.dl`
2. must be defined as `- int_A^B E.dl`
3. is zero.
4. can have a non-zero value.

Prove that a closed equipotential surface with no charge within itself must enclose an equipotential volume.

Find the equation of the equipotentials for an infinite cylinder of radius r₀, carrying charge of linear density λ.

Two identical current carrying coaxial loops, carry current I in an opposite sense. A simple amperian loop passes through both of them once. Calling the loop as C ______.

1. `oint B.dl = +- 2μ_0I`
2. the value of `oint B.dl` is independent of sense of C.
3. there may be a point on C where B and dl are perpendicular.
4. B vanishes everywhere on C.

An e.m.f is produced in a coil, which is not connected to an external voltage source. This can be due to ______.

1. the coil being in a time varying magnetic field.
2. the coil moving in a time varying magnetic field.
3. the coil moving in a constant magnetic field.
4. the coil is stationary in external spatially varying magnetic field, which does not change with time.

A circular coil expands radially in a region of magnetic field and no electromotive force is produced in the coil. This can be because ______.

1. the magnetic field is constant.
2. the magnetic field is in the same plane as the circular coil and it may or may not vary.
3. the magnetic field has a perpendicular (to the plane of the coil) component whose magnitude is decreasing suitably.
4. there is a constant magnetic field in the perpendicular (to the plane of the coil) direction.

Find the current in the wire for the configuration shown in figure. Wire PQ has negligible resistance. B, the magnetic field is coming out of the paper. θ is a fixed angle made by PQ travelling smoothly over two conducting parallel wires separated by a distance d.

A magnetic field B = B_o sin ( ωt )`hatk` wire AB slides smoothly over two parallel conductors separated by a distance d (Figure). The wires are in the x-y plane. The wire AB (of length d) has resistance R and the parallel wires have negligible resistance. If AB is moving with velocity v, what is the current in the circuit. What is the force needed to keep the wire moving at constant velocity?

A rectangular loop of wire ABCD is kept close to an infinitely long wire carrying a current I(t) = Io (1 – t/T) for 0 ≤ t ≤ T and I(0) = 0 for t > T (Figure). Find the total charge passing through a given point in the loop, in time T. The resistance of the loop is R.

A rod of mass m and resistance R slides smoothly over two parallel perfectly conducting wires kept sloping at an angle θ with respect to the horizontal (Figure). The circuit is closed through a perfect conductor at the top. There is a constant magnetic field B along the vertical direction. If the rod is initially at rest, find the velocity of the rod as a function of time.

Find the current in the sliding rod AB (resistance = R) for the arrangement shown in figure. B is constant and is out of the paper. Parallel wires have no resistance. v is constant. Switch S is closed at time t = 0.

Find the current in the sliding rod AB (resistance = R) for the arrangement shown in figure. B is constant and is out of the paper. Parallel wires have no resistance. v is constant. Switch S is closed at time t = 0.

Two source S₁ and S₂ of intensity I₁ and I₂ are placed in front of a screen [Figure (a)]. The pattern of intensity distribution seen in the central portion is given by Figure (b).

(a)

(b)

1. S₁ and S₂ have the same intensities.
2. S₁ and S₂ have a constant phase difference.
3. S₁ and S₂ have the same phase.
4. S₁ and S₂ have the same wavelength.

The binding energy of a H-atom, considering an electron moving around a fixed nuclei (proton), is B = `- (Me^4)/(8n^2ε_0^2h^2)`. (m = electron mass). If one decides to work in a frame of reference where the electron is at rest, the proton would be moving around it. By similar arguments, the binding energy would be

B = `- (Me^4)/(8n^2ε_0^2h^2)` (M = proton mass)

This last expression is not correct because ______.