A rectangular coil of length 0.12 m and width 0.1 m having 50 turns of wire is suspended vertically in a uniform magnetic field of strength 0.2 Wb/m². The coil carries a current of 2 A. If the plane of the coil is inclined at an angle of 30° with the direction of the field, the torque required to keep the coil in stable equilibrium will be:

1. 0.15 Nm

2. 0.20 Nm

3. 0.24 Nm

4. 0.12 Nm

In an ammeter 0.2% of main current passes through the galvanometer. If resistance of galvanometer is G, the resistance of ammeter will be

1. $\frac{1}{499}G$

2. $\frac{499}{500}G$

3. $\frac{1}{500}G$

4. $\frac{500}{499}G$

Two identical long conducting wires AOB and COD are placed at right angle to each other, with one above other such that O is their common point for the two. The wires carry  I₁ and I₂ currents, respectively. Point P is lying at distance d from 0 along a direction perpendicular to the plane containing the wires. The magnetic field at the point P will be

1. μ_o/2πd(I₁/I₂)
 

2. μ_o/2πd (I₁+I₂)
 

3. μ_o/2πd(I₁²-I₂²)
 

4. μ_o/2πd(I₁²+I₂²)^1/2

 

A current loop in a magnetic field

1. experiences a torque whether the field is uniform or non-uniform in all orientations

2. can be in equilibrium in one orientation.

3. can be equilibrium in two orientations; both the equilibrium states are unstable

4. can be in equilibrium in two orientations, one stable while the other is unstable

A bar magnet of length L and magnetic dipole moment M is bent in the form of an are as shown in figure. The new magnetic dipole moment will be


1. M
2. 3M/π
3. 2/πM
4. M/2

Two similar coils of radius R are lying concentrically with their planes at right angles to each other. The currents flowing in them are I and 2I, respectively. The resultant magnetic field induction at the centre will be 

1. $\frac{\sqrt{5}{\mu }_{0}I}{2R}$                                         

2. $\frac{3{\mu }_{0}I}{2R}$

3. $\frac{{\mu }_{0}I}{2R}$                                             

4. $\frac{{\mu }_{0}I}{R}$

An alternating electric field of frequency v, is applied across the dees (radius=R) of a cyclotron that is being used to accelerate protons(mass=m).The operating magnetic field (B) used in the cyclotron and the kinetic energy (K) of the proton beam, produced by it, are given by

1. B=$\frac{mv}{e}<mspace\; width="1em"></mspace>and<mspace\; width="1em"></mspace>K=2m{\mathrm{\pi }}^2{\mathrm{v}}^2{\mathrm{R}}^2$

2. B=$\frac{2\mathrm{\pi }mv}{e}<mspace\; width="1em"></mspace>and<mspace\; width="1em"></mspace>K=m^2{\mathrm{\pi vR}}^2$

3. B=$\frac{2\mathrm{\pi }mv}{e}<mspace\; width="1em"></mspace>and<mspace\; width="1em"></mspace>K=2m{\mathrm{\pi }}^2{\mathrm{v}}^2{\mathrm{R}}^2$

4. B=$\frac{mv}{e}<mspace\; width="1em"></mspace>and<mspace\; width="1em"></mspace>K=m^2{\mathrm{\pi vR}}^2$

A proton carrying 1 MeV kinetic energy is moving in a circular path of radius R in a uniform magnetic field. What should be the energy of an $\mathrm{\alpha }$-particle to describe a circle of the same radius in the same field?

1. 2 MeV                 
2. 1 MeV
3. 0.5 MeV               
4. 4 MeV

A current-carrying closed loop in the form of a right-angle isosceles triangle ABC is placed in a uniform magnetic field acting along AB. If the magnetic force on the arm BC is F, the force on the arm AC is:

1. $\mathbf{-}\mathbf{F}$                                               2. $\mathbf{F}$

3. $\sqrt{2}\mathbf{F}$                                             4. $-\sqrt{2}\mathbf{F}$

A uniform electric field and a uniform magnetic field are acting in the same direction in a certain region. If an electron is projected in the region such that its velocity is pointed along the direction of fields, then the electron :

1. speed will decrease

2. speed will increase 

3. will turn towards the left of the direction of motion 

4. will turn towards right of direction a motion