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Two similar coils of radius R are lying concentrically with
their planes at right angles to each other. The current
flowing in them are 3I and 4I respectively. The resultant
magnetic field induction at the centre is
1. $\frac{{\mathrm{\mu }}_0\mathrm{I}}{\mathrm{\pi }}$
2. $\frac{5{\mathrm{\mu }}_0\mathrm{I}}{2\mathrm{R}}$
3. $\frac{7{\mathrm{\mu }}_0\mathrm{I}}{2\mathrm{R}}$
4. zero

A current carrying closed Loop in the form of a right isosceles triangle ABC is placed in xy plane in a uniform magnetic field acting along y-axis as shown in figure. If the magnetic force on the arm AC is $\overrightarrow{F}$ , then force on the arm BC and AB are respectively

1. zero, zero
2. -$\overrightarrow{F}$ and zero
3. $\overrightarrow{F}$ and -$\overrightarrow{F}$
4. $\overrightarrow{F}$ and zero

When a proton is released from rest in a room, it starts with an initial acceleration a₀ towards east. When it is projected towards north with a speed v₀ , it moves with initial acceleration 3a₀ towards east. The electric and magnetic fields in the room are
1. $\frac{{\mathrm{Ma}}_0}{\mathrm{e}} west,\frac{2{\mathrm{Ma}}_0}{{\mathrm{ev}}_0} up$
2. $\frac{{\mathrm{Ma}}_0}{\mathrm{e}} west,\frac{2{\mathrm{Ma}}_0}{{\mathrm{ev}}_0} \mathrm{down}$
3. $\frac{{\mathrm{Ma}}_0}{\mathrm{e}} \mathrm{ea}st,\frac{2{\mathrm{Ma}}_0}{{\mathrm{ev}}_0} up$
4. $\frac{{\mathrm{Ma}}_0}{\mathrm{e}} \mathrm{ea}st,\frac{2{\mathrm{Ma}}_0}{{\mathrm{ev}}_0} \mathrm{down}$

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 megnetic field with a velocity 2v,
then its time period will be
1. 2 T 
2. 4 T
3. T/2
4.  T

A circular coil of radius R is carrying a certain current. At
a point on its axis at distance x from centre the value of
magnetic field is found to be $\frac{1}{2\sqrt{2}}$ times the magnetic
field at its centre. The value of x must be
1. R
2. 2R
3. 3R
4. R/2

The magnetic dipole moment of the given loop is

1. $\frac{5}{2}{\mathrm{\pi R}}^2\mathrm{I}$
2. $3{\mathrm{\pi R}}^2\mathrm{I}$
3. $\frac{3}{2}{\mathrm{\pi R}}^2\mathrm{I}$
4. $5{\mathrm{\pi R}}^2\mathrm{I}$

A short magnetic dipole is placed at the origin with its dipole
moment directed along the x-axis. If magnetic field
induction at a point P (r, o) is B$\hat{\mathrm{i}}$, then the magnetic field
induction at point Q(0,2r) will be:
1. $-\frac{\mathrm{B}}{16}\hat{\mathrm{i}}$
2. $-\frac{\mathrm{B}}{16}\hat{j}$
3. $\frac{\mathrm{B}}{16}\hat{\mathrm{i}}$
4. $\frac{\mathrm{B}}{16}\hat{j}$

If an electron enters a magnetic field with its velocity pointing
in the same direction as the magnetic field then :–
1. the electron will turn towards right
2. the electron will turn towards left
3. the velocity of the electron will increase
4. the velocity of the electron will remain
unchanged

A and B are two concentric circular loop carrying current
i₁ and i₂ as shown in figure. If ratio of their radii is 1:2
and ratio of the flux densities at the centre O due to A
and B is 1:3 then the value of $\frac{{\mathrm{i}}_1}{{\mathrm{i}}_2}$ will be :-

1. $\frac{1}{2}$
2. $\frac{1}{3}$
3. $\frac{1}{4}$
4. $\frac{1}{6}$

Current I is flowing in a conducting circular loop of
radius R. It is kept in a magnetic field B which is
perpendicular to the plane of a circular loop, the magnetic
force acting on the loop is:
1. IRB 
2. 2 $\mathrm{\pi }$IRB
3. Zero 
4. $\mathrm{\pi }$ IRB

The vector form of Biot Savart's law for a current carrying
element is :-
1. $\overrightarrow{\mathrm{dB}}=\frac{{\mu }_0}{4\pi }\frac{idl \sin \varphi }{r^2}$
2. $\overrightarrow{\mathrm{dB}}=\frac{{\mu }_0}{4\pi }\frac{i\overrightarrow{dl }\mathit{\times }\hat{\mathit{r}}}{r^2}$
3. $\overrightarrow{\mathrm{dB}}=\frac{{\mu }_0}{4\pi }\frac{i\overrightarrow{dl }\mathit{\times }\hat{r}}{r^3}$
4.  $\overrightarrow{\mathrm{dB}}=\frac{{\mu }_0}{4\pi }\frac{i\overrightarrow{dl }\mathit{\times }\overrightarrow{\mathit{r}}}{r^2}$

A long solenoid has length L, average diameter D and
n layer of turns. Each layer contains N turns. If the current
flowing through the solenoid is I, the value of the magnetic
field at the centre :
1. Proportional to D
2. Inversely proportional to D
3. Does not depend on D
4. Proportional to L

For the given current distribution the magnetic field at
point, 'P' is :-

1. $\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\odot$
2. $\frac{{\mathrm{\mu }}_0}{\mathrm{\pi }}\otimes$
3. $\frac{{\mathrm{\mu }}_0}{2\mathrm{\pi }}\otimes$
4. $\frac{{\mathrm{\mu }}_0}{2\mathrm{\pi }}\odot$

Two particles x and y have equal charges and possessing
equal kinetic energy enter in a uniform magnetic field
and describe circular path of radius of curvature r₁
and r₂ respectively. The ratio of their masses is :–
1. $\left(\frac{{\mathrm{r}}_1}{{\mathrm{r}}_2}\right)$
2. ${\left(\frac{{\mathrm{r}}_1}{{\mathrm{r}}_2}\right)}^{1/2}$
3. ${\left(\frac{{\mathrm{r}}_1}{{\mathrm{r}}_2}\right)}^2$
4. $\left(\frac{{\mathrm{r}}_2}{{\mathrm{r}}_1}\right)$

An electron having mass 'm' and kinetic energy E enter in uniform magnetic field B perpendicularly, then its frequency of uniform circular motion will be :–
1. $\frac{\mathrm{eE}}{\mathrm{qVB}}$
2. $\frac{2\mathrm{\pi m}}{\mathrm{eB}}$
3. $\frac{\mathrm{eB}}{2\mathrm{\pi m}}$
4. $\frac{2\mathrm{m}}{\mathrm{eBE}}$
 

If number of turn, area and current through the coil is given by n, A and i respectively then its magnetic moment will be :–
1. niA 
2. n²iA
3. niA²
4. $\frac{\mathrm{ni}}{\sqrt{\mathrm{A}}}$

Magnetic field at point O will be :-

1. $\frac{{\mathrm{\mu }}_0\mathrm{I}}{2\mathrm{R}}\otimes$
2. $\frac{{\mathrm{\mu }}_0\mathrm{I}}{2\mathrm{R}}\odot$
3. $\frac{{\mathrm{\mu }}_0\mathrm{I}}{2\mathrm{R}}\left(1-\frac{1}{\mathrm{\pi }}\right)\otimes$
4. $\frac{{\mathrm{\mu }}_0\mathrm{I}}{2\mathrm{R}}\left(1+\frac{1}{\mathrm{\pi }}\right)\otimes$

A coil of one loop is made by a wire of length L and there after a coil of two loops is made by same wire. The ratio of magnetic field at the centre of coils respectively :-
1. 1 : 4 
2. 1 : 1
3. 1 : 8 
4. 4 : 1

Radius of a current carrying coil is ‘R’. The ratio of magnetic field at a axial point which is R distance away from the centre of the coil to the magnetic field at the centre of the coil :-
1. ${\left(\frac{1}{2}\right)}^{1/2}$
2. $\frac{1}{2}$
3. ${\left(\frac{1}{2}\right)}^{3/2}$
4. $\frac{1}{4}$

An electric field E and a magnetic field B applied on a
proton which moves with velocity v, it goes undeflected
through the region if :-
1. E $\perp$ B
2. E is parallel to v and perpendicular to B
3.  E, B and v all three mutually perpendicular
    to each other and $\mathrm{v}=\frac{\mathrm{E}}{\mathrm{B}}$
4.  E and B both are parallel but perpendicular to v