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 orentations.

(3) can be equilibrium in two orientations, both the wquilibriu 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=$\frac{mv}{e} and K=2m{\mathrm{\pi }}^2{\mathrm{v}}^2{\mathrm{R}}^2$

(2)B=$\frac{2\mathrm{\pi }mv}{e} and K=m^2{\mathrm{\pi vR}}^2$

(3)B=$\frac{2\mathrm{\pi }mv}{e} and K=2m{\mathrm{\pi }}^2{\mathrm{v}}^2{\mathrm{R}}^2$

(4)B=$\frac{mv}{e} and K=m^2{\mathrm{\pi vR}}^2$

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