A circuit contains an ammeter, a battery of 30 V and a resistance 40.8Ω all connected in series. If the ammeter has a coil of resistance 480Ω  and a shunt of 20Ω then reading in the ammeter will be :

1. 0.5A
 

2. 0.25A

3. 2A
 

4. 1A

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

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

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 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