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

A square loop, carrying a steady current I, is placed in a horizontal plane near a long straight conductor carrying a steady current $I_{\mathit{1}}$ at a distance d from the conductor as shown in figure. The loop will experience 

(1) a net repulsive force away from the conductor 

(2) a net torque acting upward perpendicular to the horizontal plane

(3) a net torque acting downward normal to the horizontal plane

(4) a net attractive force towards the conductor 

Charge q is uniformly spread on a thin ring of radius R. The ring rotates about its axis with a uniform frequency f Hz. The magnitude of magnetic induction at the center of the ring is :

(1) $\frac{{\mathrm{\mu }}_0\mathrm{q} f}{2\mathrm{R}}$                                       

(2) $\frac{{\mathrm{\mu }}_0\mathrm{q}}{2f\mathrm{R}}$

(3) $\frac{{\mathrm{\mu }}_0\mathrm{q}}{2\mathrm{\pi }f\mathrm{R}}$                                       

(4) $\frac{{\mathrm{\mu }}_0\mathrm{q} f}{2\mathrm{\pi R}}$

A beam of cathode rays is subjected to crossed Electric (E) and magnetic fields(B). The fields are adjusted such that the beam is not deflected. The specific charge of the cathode rays is given by:

1. $\frac{B^2}{2V{E}^2}$                                             

2. $\frac{2V{B}^2}{E^2}$

3. $\frac{2V{E}^2}{B^2}$                                           

4. $\frac{E^2}{2V{B}^2}$

(where V is the potential difference between cathode and anode)

A conducting circular loop is placed in a uniform magnetic field, \(B=0.025\) T with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of \(1\) mm/s. The induced emf when the radius is \(2\) cm, is:
1. \(2\pi\) \(\mu\)V
2. \(\pi \) \(\mu\)V
3. \(\frac{\pi}{2}\) \(\mu\)V
4. \(2\) \(\mu\)V