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 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)$\frac{{\mu }_{0}I}{R}$

A millivoltmeter of 25 mV range is to be converted into an ammeter of 25 A range. The value (in ohm) of necessary shunt will be:

(1)0.001                                     

(2)0.01

(3)1                                           

(4)0.05

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 galvanometer of resistance, G is shunted by a resistance S ohm. To keep the main current in the circuit unchanged, the resistance to be put in series with the galvanometer is

(1) $\frac{S^{\mathit{2}}}{(S+G)}$                                             

(2) $\frac{SG}{(S+G)}$

(3) $\frac{G^{\mathit{2}}}{(S+G)}$                                             

(4) $\frac{G}{(S+G)}$

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