A current loop consists of two identical semicircular parts each of radius \(R\), one lying in the \(x\text-y\) plane, and the other in the \(x\text-z\) plane. If the current in the loop is \(i\), what will be the resultant magnetic field due to the two semicircular parts at their common centre?

1.	\( \dfrac{\mu_0 i}{2 \sqrt{2} R} \)	2.	\( \dfrac{\mu_0 i}{2 R} \)
3.	\( \dfrac{\mu_0 i}{4 R} \)	4.	\( \dfrac{\mu_0 i}{\sqrt{2} R}\)

A closely wound solenoid of 2000 turns and area of cross-section $1.5\times {10}^{-4} {\mathrm{m}}^2$ carries a current of $2.0 \mathrm{A}.$ It is suspended through its centre and perpendicular to its length, allowing it to turn in a horizontal plane in a uniform magnetic field $5\times {10}^{-2} \mathrm{T}$ making an angle of $30°$ with the axis of the solenoid. The torque on the solenoid will be

(1) $3\times {10}^{-3} \mathrm{N}‐\mathrm{m}$                                 

(2) $1.5\times {10}^{-3} \mathrm{N}‐\mathrm{m}$

(3) $1.5\times {10}^{-2} \mathrm{N}‐\mathrm{m}$                               

(4) $3\times {10}^{-2} \mathrm{N}‐\mathrm{m}$

A particle having a mass of ${10}^{-2} \mathrm{kg}$carries a charge of $5\times {10}^{-8} \mathrm{C}.$ The particle is given an initial horizontal velocity of ${10}^5 {\mathrm{ms}}^{-1}$ in the presence of electric field $\overrightarrow{\mathbf{E}}$ and magnetic field $\overrightarrow{\mathbf{B}}$. To keep the particle moving in a horizontal direction, it is necessary that

(1) $\overrightarrow{\mathbf{B}}$ should be perpendicular to the direction of velocity and $\overrightarrow{\mathbf{E}}$ should be along the direction of velocity.

(2) Both $\overrightarrow{\mathbf{B}}$ and $\overrightarrow{\mathbf{E}}$ should be along the direction of velocity.

(3) Both $\overrightarrow{\mathbf{B}}$ and $\overrightarrow{\mathbf{E}}$ are mutually perpendicular and perpendicular to the direction of velocity.

(4) $\overrightarrow{\mathbf{B}}$ should be along the direction of velocity and $\overrightarrow{\mathbf{E}}$ should be perpendicular to the direction of velocity.

Which one of the following pairs of statements are possible?

1.   (1) and (3)                                       2.    (3) and (4)

3.   (2) and (3)                                       4.   (2) and (4)

Under the influence of a uniform magnetic field, a charged particle moves with constant speed v in a circle of radius R. The time period of rotation of the particle -

1. depends on v and not on R

2. depends on R and not on v

3. is independent of both v and R

4. depends on both v and R

The magnetic force acting on a charged particle of charge $-2\mu C$ in a magnetic field of 2T acting in y-direction, when the particle velocity is $\left(2\hat{i}+3\hat{j}\right)\times {10}^6 m{s}^{-1}$ is.

1. 8 N in -z-direction

2. 4 N in z-direction

3. 8 N in y-direction

4. 4 N in y-direction

A galvanometer having a coil resistance of $60\Omega$ shows full scale deflection when a current of 1.0A passes through it. It can be converted into an ammeter to read currents upto 5.0A by 

(a) putting in series resistance of 240$\Omega$

(b) putting in parallel resistance of 240$\Omega$

(c) putting in series resistance of 15$\Omega$

(d) putting in parallel resistance of 15$\Omega$

A closed-loop PQRS carrying a current is placed in a uniform magnetic field. If the magnetic forces on segments PS, SR and RO are $F_1, F_2 and F_3$ respectively and are in the plane of the paper and along with the directions shown the force on the segment QP is 

(a)$F_3+F_1-F_2$

(b)$\sqrt{{\left(F_3-F_1\right)}^2+F_2^2}$

(c)$\sqrt{{\left(F_3-F_1\right)}^2-F_2^2}$

(d)$F_3-F_1+F_2$

A particle mass m, charge Q, and kinetic energy T enter a transverse uniform magnetic field of induction $\overrightarrow{B}$. After 3sec the kinetic energy of the particle will be : 

1. 3T

2. 2T

3. T

4. 4T

A galvanometer of resistance 50$\Omega$ is connected to a battery of 3 V along with a resistance of 2950 $\Omega$ in series. A full-scale deflection of 30 divisions is obtained in the galvanometer. In order to reduce this deflection to 20 divisions, the resistance in series should be 

(a) 5050$\Omega$

(b) 5550 $\Omega$

(c) 6050 $\Omega$

(d) 4450$\Omega$

 A narrow electron beam passes undeviated through an electric field E = $3\times {10}^4 \mathrm{volt}/\mathrm{m}$ and an overlapping magnetic field $\mathrm{B}=2\times {10}^{-3} \mathrm{Weber}/{\mathrm{m}}^2$. If electric field and magnetic field are mutually perpendicular. The speed of the electrons is 
1. \(60\) m/s                       
2. $10.3\times {10}^7 \mathrm{m}/\mathrm{s}$
3. $1.5\times {10}^7 \mathrm{m}/\mathrm{s}$             
4. $0.67\times {10}^{-7 }\mathrm{m}/\mathrm{s}$