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What is the net force on the square coil?
              

(1) $1.67\times {10}^{-6}N$ moving towards wire
(2) $25\times {10}^{-7}N$ moving away from wire
(3) $35\times {10}^{-7}N$ moving towards wire
(4) $35\times {10}^{-7}N$ moving away from wire

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. $-\sqrt{2}\mathbf{F}$

Order of q/m ratio of proton, $\alpha$-particle and electron is
(a) $\mathrm{e}>\mathrm{p}>\mathrm{\alpha }$               (b) $\mathrm{p}>\mathrm{\alpha }>\mathrm{e}$
(c) $\mathrm{e}>\mathrm{\alpha }>\mathrm{p}$               (d) None of these

When an electron enters perpendicularly in a magnetic field with velocity v, time period of its revolution is T. If it enters in the same magnetic field with a velocity 2v, then its time period will be:
1.  2T
2.  4T
3.  $\frac{\mathrm{T}}{2}$
4.   T

An electron is traveling along the x-direction. It encounters a magnetic field in the y-direction. Its subsequent motion will be:
1.  Straight-line along the x-direction
2.  A circle in the xz-plane
3.  A circle in the yz-plane
4.  A circle in the xy-plane
 

A closed-loop (of any shape) carrying current lies in the x-y plane. What happens when a uniform magnetic field B is present in the region such that the loop experiences zero force?

A circular coil of wire of radius 'r' has 'n' turns and carries a current 'I'. The magnetic induction (B) at a point on the axis of the coil at a distance $\sqrt{3}r$ from its center is :
1.  $\frac{{\mathrm{\mu }}_0\mathrm{In}}{4\mathrm{r}}$
2.  $\frac{{\mathrm{\mu }}_0\mathrm{In}}{8\mathrm{r}}$
3.  $\frac{{\mathrm{\mu }}_0\mathrm{In}}{16\mathrm{r}}$
4.  $\frac{{\mathrm{\mu }}_0\mathrm{In}}{32\mathrm{r}}$

The dots in the figure depict a magnetic field that is perpendicular to the plane of the paper and emanates from it. The trajectory of a particle in the plane of the paper is depicted by the curve ABC. What exactly is the particle?
                           

If an electron of velocity $\left(2\hat{\mathrm{i}}\right)$ $+$ $3\hat{j}$ is subjected to a magnetic field of \(4\hat{\mathrm{k}}\) :

Below figures (1) and (2) represent lines of force. Which is correct statement  ?

(1) Figure (1) represents magnetic lines of force
(2) Figure (2) represents magnetic lines of force
(3) Figure (1) represents electric lines of force
(4) Both figure (1) and figure (2) represent magnetic lines of force

The magnetic induction at point P, which is 4 cm from a long current-carrying wire is 10^-8 Tesla. What would be the field of induction at a distance of 12 cm from the same current?

Two straight horizontal parallel wires carry the same current in the same direction, and d is the distance between them. You are given a small magnetic needle that is freely suspended. Which of the following positions will have the needle's orientation independent of the magnitude of the current in the wires?

In the figure shown, the magnetic induction at the centre of the arc due to the current in portion AB will be

(a) $\frac{{\mathrm{\mu }}_0\mathrm{i}}{\mathrm{r}}$                       (c)  $\frac{{\mathrm{\mu }}_0\mathrm{i}}{4\mathrm{r}}$
(b) $\frac{{\mathrm{\mu }}_0\mathrm{i}}{2\mathrm{r}}$                        (d) Zero

In a current-carrying long solenoid, the field produced does not depend upon:

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) $\frac{500}{499}G$

If the current is flowing in the south direction along a power line, then what will be the direction of the magnetic field above the power line (neglecting the earth's field)?

An electron and a proton with equal momentum enter perpendicularly into a uniform magnetic field, then :
(1) The path of proton shall be more curved than that of electron
(2) The path of proton shall be less curved than that of electron
(3) Both are equally curved
(4) Path of both will be a straight line

Two particles A and B of masses $m_A$ and $m_B$ respectively and having the same type of charge are moving in a plane. A uniform magnetic field exists perpendicular to this plane. The speeds of the particles are $v_A$ and $v_B$ respectively, and the trajectories are as shown in the figure. Then
                                
(1) $m_A{v}_A<m_B{v}_B$                              
(2) $m_A{v}_A>m_B{v}_B$
(3) $m_A<m_B and v_A<v_B$                  
(4) $m_A=m_B and v_A=v_B$

An electric current passes through a long straight wire. At a distance 5 cm from the wire, the magnetic field is B. The field at 20 cm from the wire would be :
(1) $\frac{\mathrm{B}}{6}$                   
(2) $\frac{\mathrm{B}}{4}$
(3) $\frac{\mathrm{B}}{3}$                     
(4) $\frac{\mathrm{B}}{2}$ 
 

Two particles X and Y having equal charges, after being accelerated through the same potential difference, enter a region of uniform magnetic field and describes circular path of radius ${\mathrm{R}}_1$ and ${\mathrm{R}}_2$ respectively. The ratio of mass of X to that of Y is :
(a)  ${\left(\frac{{\mathrm{R}}_1}{{\mathrm{R}}_2}\right)}^{1/2}$                         (b)  $\frac{{\mathrm{R}}_2}{{\mathrm{R}}_1}$
(c)  ${\left(\frac{{\mathrm{R}}_1}{{\mathrm{R}}_2}\right)}^2$                             (d)  $\frac{{\mathrm{R}}_1}{{\mathrm{R}}_2}$  

Two thin long parallel wires separated by a distance b are carrying a current i amp each. The magnitude of the force per unit length exerted by one wire on the other is
(1) $\frac{{\mu }_0{i}^2}{b^2}$                                 
(2) $\frac{{\mu }_0{i}^2}{2\mathrm{\pi b}}$ 
(3) $\frac{{\mu }_{0}i}{2\mathrm{\pi b}}$                                  
(4) $\frac{{\mu }_{0}i}{2{\mathrm{\pi b}}^2}$ 

A small coil of N turns has an effective area A and carries a current I. It is suspended in a horizontal magnetic field $\stackrel{.}{B}$ such that its plane is perpendicular to $\stackrel{.}{B}$. The work done in rotating it by $180°$ about the vertical axis is 
(a) $NAIB$                               (b) $2NAIB$ 
(c) $2\mathrm{\pi NAIB}$                          (d) $4\mathrm{\pi }NAIB$

Which among the following options needs to be decreased to increase the sensitivity of a moving coil galvanometer?

An electron, moving in a uniform magnetic field of induction of intensity $\stackrel{\rightharpoonup }{B,}$ has its radius directly proportional to :
(1) Its charge                       
(2) Magnetic field
(3) Speed                               
(4) None of these

A particle of charge q and mass m is moving along the x-axis with a velocity of v and enters a region of electric field E and magnetic field B as shown in the figure below. For which figure is the net force on the charge zero?

1.		2.
3.		4.

 A long straight wire along the z-axis carries a current I in the negative z-direction. The magnetic field vector $\overrightarrow{\mathrm{B}}$ at a point having coordinates (x, y) in the z = 0 plane is :
1. $\frac{{\mathrm{\mu }}_0\mathrm{I}(\mathrm{y}\hat{\mathrm{i}}-\mathrm{x}\hat{\mathrm{j}})}{2\mathrm{\pi }({\mathrm{x}}^2+{\mathrm{y}}^2)}$                 
2. $\frac{{\mathrm{\mu }}_0\mathrm{I}(\mathrm{x}\hat{\mathrm{i}}+\mathrm{y}\hat{\mathrm{j}})}{2\mathrm{\pi }({\mathrm{x}}^2+{\mathrm{y}}^2)}$
3. $\frac{{\mathrm{\mu }}_0\mathrm{I}(\mathrm{x}\hat{\mathrm{j}}-\mathrm{y}\hat{\mathrm{i}})}{2\mathrm{\pi }({\mathrm{x}}^2+{\mathrm{y}}^2)}$                 
4. $\frac{{\mathrm{\mu }}_0\mathrm{I}(\mathrm{x}\hat{\mathrm{i}}-\mathrm{y}\hat{\mathrm{j}})}{2\mathrm{\pi }({\mathrm{x}}^2+{\mathrm{y}}^2)}$

Figure shows a square loop ABCD with edge length a. The resistance of the wire ABC is r
and that of ADC is 2r. The value of magnetic field at the centre of the loop assuming
uniform wire is
                   
1. $\frac{\sqrt{2}{\mu }_{0}i}{3\mathrm{\pi a}}\odot$                                 
2. $\frac{\sqrt{2}{\mu }_{0}i}{3\mathrm{\pi a}}\otimes$
3. $\frac{\sqrt{2}{\mu }_{0}i}{\mathrm{\pi a}}\odot$                                   
4. $\frac{\sqrt{2}{\mu }_{0}i}{\mathrm{\pi a}}\otimes$   

A particle with charge q, moving with a momentum p, enters a uniform magnetic field normally. The magnetic field has magnitude B and is confined to a region of width d, where $d<\frac{p}{Bq}$. The particle is deflected by an angle $\theta$ in crossing the field, then:
  

The unit vectors $\hat{i}, \hat{j} and \hat{k}$ are as shown below. What will be the magnetic field at O in the following figure?

(a) $\frac{{\mu }_0}{4\mathrm{\pi }}\frac{i}{a}\left(2-\frac{\mathrm{\pi }}{2}\right)\hat{j}$             (b) $\frac{{\mu }_0}{4\mathrm{\pi }}\frac{i}{a}\left(2+\frac{\mathrm{\pi }}{2}\right)\hat{j}$
(c) $\frac{{\mu }_0}{4\mathrm{\pi }}\frac{i}{a}\left(2+\frac{\mathrm{\pi }}{2}\right)\hat{i}$              (d) $\frac{{\mu }_0}{4\mathrm{\pi }}\frac{i}{a}\left(2+\frac{\mathrm{\pi }}{2}\right)\hat{k}$ 

A current I is carried by an elastic circular wire of length L. It is placed in a uniform magnetic field B (out of paper) with its plane perpendicular to B's direction. What will happen to the wire?
       \(F ~\)

Two particles each of mass m and charge q are attached to the two ends of a light rigid rod of length 2R. The rod is rotated at constant angular speed about a perpendicular axis passing through its centre. The ratio of the magnitudes of the magnetic moment of the system and its angular momentum about the centre of the rod is:
1. $\frac{q}{2m}$                               
2. $\frac{q}{m}$
3. $\frac{2q}{m}$                              
4. $\frac{q}{\mathrm{\pi m}}$ 

Three long, straight parallel wires carrying current, are arranged as shown in figure. The force experienced by a 25 cm length of wire C is
 
(1) ${10}^{-3}N$
(2) $2.5\times {10}^{-3}N$
(3) Zero
(4) $1.5\times {10}^{-3}N$

When a proton is released from rest in a room, it starts with an initial acceleration $a_o$ towards west. When it is projected towards north with a speed $v_o$ , it moves with an initial acceleration 3$a_o$ towards west. The electric and magnetic fields in the room are 
(a) ma_o/e west, 4ma_o/ev_o up
(b) ma_o/e west, 2ma_o/ev_o down
(c) ma_o/e east, 3ma_o/ev_o up
(d) ma_o/e east, 3ma_o/ev_o down

Two wires are held perpendicular to the plane at 5m apart. They carry currents of 2.5 A and 5A in same direction. Then the magnetic field strength (B) at a point midway between the wires will be -
1. $\frac{{\mathrm{\mu }}_0\mathrm{T}}{4\mathrm{\pi }}T$
2. $\frac{{\mathrm{\mu }}_0}{2\mathrm{\pi }}T$
3. $\frac{3{\mathrm{\mu }}_0}{2\mathrm{\pi }}T$
4. $\frac{3{\mathrm{\mu }}_0}{4\mathrm{\pi }}T$

An electron moves with a velocity $1\times {10}^3 m s^{-1}$ in a magnetic field of induction 0.3 T at an angle $30°. \mathrm{If} \frac{\mathrm{e}}{\mathrm{m}}$ of electron is $1.76\times {10}^{11}C k{g}^{-1}$, the radius of the path is nearly
1. ${10}^8$m
2. $2\times {10}^{-8}$m
3. ${10}^{-8}$m
4. ${10}^{-10}$m

A charged particle of charge q and mass m enters perpendicularly in a magnetic field $\overrightarrow{\mathrm{B}}$. Kinetic energy of the particle is E; then frequency of rotation is
1. $\frac{\mathrm{qB}}{\mathrm{m\pi }}$
2. $\frac{\mathrm{qB}}{2\mathrm{\pi m}}$
3. $\frac{\mathrm{qBE}}{2\mathrm{\pi m}}$
4. $\frac{\mathrm{qB}}{2\mathrm{\pi E}}$

A galvanometer of $50\mathrm{\Omega }$ resistance has 25 divisions. A current of $4\times {10}^{-4}$ gives a deflection of one division. To convert this galvanometer into a voltmeter having a range of 25 V, it should be connected with a resistance of
1. $245\mathrm{\Omega }$ as a shunt
2. $2550\mathrm{\Omega }$ in series
3. $2450\mathrm{\Omega }$ in series
4. $2550\mathrm{\Omega }$ as a shunt

When a charged particle moving with velocity $\overrightarrow{\mathrm{v}}$ is subjected to a magnetic field of induction $\overrightarrow{\mathrm{B}}$, the force on it is non-zero. This implies the
1. angle between $\overrightarrow{\mathrm{v}} and \overrightarrow{B}$ is necessary $90°$.
2. angle between $\overrightarrow{\mathrm{v}} and \overrightarrow{B}$ can have any value other than $90°$.
3. angle between $\overrightarrow{\mathrm{v}} and \overrightarrow{B}$ can have any other value than zero and $180°$.
4. angles between $\overrightarrow{\mathrm{v}} and \overrightarrow{B}$ is either zero or $180°$.

A galvanometer having a coil resistance of $60\mathrm{\Omega }$ shows full scale deflection when a current of 1.0 A passes through it. It can be converted into an ammeter to read current up to 5.0A by
1. putting in series a resistance of $15\mathrm{\Omega }$.
2. putting in series a resistance of $240\mathrm{\Omega }$.
3. putting in parallel a resistance of $15\mathrm{\Omega }$.
4. putting in parallel a resistance of $240\mathrm{\Omega }$.

A galvanometer has a coil of resistance 100 ohm and gives a full scale deflection for a 30 mA current. If it is used as a voltmeter of 30 volt range, the resistance required to be added will be
1. $1000\mathrm{\Omega }$
2. $900\mathrm{\Omega }$
3. $1800\mathrm{\Omega }$
4. $500\mathrm{\Omega }$

A current loop consists of two identical semicircular parts each of radius R, one lying in the x-y plane and the other in y-z plane. If the current in the loop is i, then, the resultant magnetic field due to the two semicircular parts at their common center is
1. $\frac{{\mathrm{\mu }}_0\mathrm{i}}{2\mathrm{R}}$
2. $\frac{{\mathrm{\mu }}_0\mathrm{i}}{4\mathrm{R}}$
3. $\frac{{\mathrm{\mu }}_0\mathrm{i}}{\sqrt{2\mathrm{R}}}$
4. $\frac{{\mathrm{\mu }}_0\mathrm{i}}{2\sqrt{2\mathrm{R}}}$

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 of the centre of the ring is
1. $\frac{{\mathrm{\mu }}_0\mathrm{qf}}{2\mathrm{\pi R}}$
2. $\frac{{\mathrm{\mu }}_0\mathrm{qf}}{2R}$
3. $\frac{{\mathrm{\mu }}_0\mathrm{q}}{2\mathrm{fR}}$
4. $\frac{{\mathrm{\mu }}_0\mathrm{q}}{2\mathrm{\pi fR}}$

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. $\frac{G}{(S+G)}$
2. $\frac{{\mathrm{S}}^2}{(S+G)}$
3. $\frac{SG}{(S+G)}$
4. $\frac{G^{\mathit{2}}}{(S+G)}$

An electron moving in a circular orbit of radius r makes n rotations per second. The magnetic field produced at the centre has magnitude
1. zero
2. $\frac{{\mathrm{\mu }}_0{\mathrm{\pi }}^2\mathrm{e}}{\mathrm{r}}$
3. $\frac{{\mathrm{\mu }}_0\mathrm{ne}}{2\mathrm{r}}$
4. $\frac{{\mathrm{\mu }}_0\mathrm{ne}}{2\mathrm{\pi r}}$

A square loop ABCD carrying a current i is placed near  coplanar long straight conductor XY carrying a current I. The net force on the loop will be -

1. $\frac{2{\mu }_{0}Ii}{3\pi }$
2. $\frac{{\mu }_{0}Ii}{\mathit{2}\pi }$
3. $\frac{2{\mu }_{0}Ii}{3\pi L}$
4. $\frac{{\mu }_{0}Ii}{\mathit{2}\pi L}$