${\mathrm{O}}^{++}, {\mathrm{C}}^{+}, {\mathrm{He}}^{++}$ and ${\mathrm{H}}^{+}$ ions are projected on the photographic plate with the same velocity in a mass spectrograph. Which one will strike the farthest?

1. ${\mathrm{O}}^{++}$                  2. ${\mathrm{C}}^{+}$
3. ${\mathrm{He}}^{++}$                4. ${\mathrm{H}}_2^{+}$

A 250-Turn rectangular coil of length 2.1 cm and width 1.25 cm carries a current of 85$\mu A$and subjected to the magnetic field of strength 0.85 T. Work done for rotating the coil by 180° against the torque is:

1. $4.55 \mu J$

2. $2.3 \mu J$

3. $1.15 \mu J$

4. $9.8 \mu J$

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. $\frac{500}{499}G$

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

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. $qvR$

In a mass spectrometer used for measuring the masses of ions, the ions are initially accelerated by an electric potential V and then made to describe semi-circular paths of radius R using a magnetic field B. If V and B are kept constant, the ratio $\frac{Charge on the ion}{mass of the ion}$, will be proportional to:

1. $\frac{1}{R}$

2. $\frac{1}{R^2}$

3. $R^2$

4. R

A cylindrical wire of radius R is carrying current i uniformly distributed over its cross-section.  If a circular loop of radius r is taken as amperian loop, then the variation value of $\oint \overrightarrow{B}.\overrightarrow{dl}$ over this loop with radius 'r' of loop will be best represented by:

(1)

(2) 

(3)

(4)

Three infinitely-long conductors carrying currents $I_1, I_2 and I_3$ lie perpendicular to the plane of the paper as shown below.

If the value of integral $\oint \overrightarrow{\mathrm{B}}.\overrightarrow{\mathrm{dl}}$ for the loops ${\mathrm{C}}_1, {\mathrm{C}}_2 \mathrm{and} {\mathrm{C}}_3 \mathrm{are} 2{\mathrm{\mu }}_0, 4{\mathrm{\mu }}_0 \mathrm{and} {\mathrm{\mu }}_0$ in the units of N/A, respectively, then

1.  $I_1$ = 3 A into the paper

2.  $l_2$ = 3 A out of the paper

3.  $I_3$ = 0

4.  $I_3$ = 1 A out of the paper

Figure shows a cross-section of a large metal sheet carrying an electric current along its surface. The current in a strip of width dl is (Kdl) where K is a constant. Find the magnetic field at a point P at a distance x from the metal strips

1.  $\frac{1}{2}{\mu }_{0}Kx$

2.  ${\mu }_{0}K$

3.  $\frac{1}{2}{\mu }_{0}K$

4.  $\frac{{\mu }_{0}Kx}{4}$

A long straight, solid metal wire of radius 2 mm carries a current uniformly distributed over its circular cross-section. The magnetic field induction at a distance 2 mm from its axis is B. Then, the magnetic field induction at distance 1 mm from axis will be

(1) B

(2) B/2

(3) 2B

(4) B