Two toroids 1 and 2 have total no. of turns 200 and 100 respectively with average radii 40 cm and 20 cm respectively. If they carry the same current i, the ratio of the magnetic fields along the two loops is:

(1) 1:1

(2) 4:1

(3) 2:1

(4) 1:2

A galvanometer has a coil of resistance 100 and gives a full-scale deflection for 30 mA current. If it is to work as a voltmeter of 30 V range, the resistance required to be added will be:

1. 900 $\Omega$

2. 1800 $\Omega$

3. 500 $\Omega$

4. 1000 $\Omega$

A current-carrying closed loop in the form of a right 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.  $-\mathrm{F}$

2.  $\mathrm{F}$

3. $2\mathrm{F}$

4.  $-2\mathrm{F}$

A charged particle (charge q) is moving in a circle of radius R with uniform speed v. The associated magnetic moment μ is given by:

1. $\frac{qvR}{2}$

2. $qv{R}^2$

3. $\frac{qv{R}^2}{2}$

4. $qvR$

A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in the equilibrium state. The energy required to rotate it by 60^o is W. Now the torque required to keep the magnet in this new position is:

1.  $\frac{W}{\sqrt{3}}$

2.  

3.  

4.  

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

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 center will be

1. $\frac{\sqrt{5}{\mu }_{0}I}{2R}$

2. $\frac{3{\mu }_{0}I}{2R}$

3. $\frac{{\mu }_{0}I}{2R}$

4. $\frac{{\mu }_{0}I}{R}$

Ionized hydrogen atoms and $\alpha$-particles with same momenta enters perpendicular to a constant magnetic field, B. The ratio of their radii of their paths $r_H:r_{\alpha }$ will be:

1. 1 : 4

2. 2 : 1

3. 1 : 2

4. 4 : 1

A metallic rod of mass per unit length 0.5 kg m^-1 is lying horizontally on a smooth inclined plane which makes an angle of 30° with the horizontal. The rod is not allowed to slide down by flowing a current through it when a magnetic field of induction 0.25 T is acting on it in the vertical direction. The current flowing in the rod to keep stationery is:

1. 7.14 A

2. 5.98 A

3. 14.76 A

4. 11.32 A