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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 31 and 41 respectively. The resultant magnetic field induction at the center is
1. $\frac{{\mu }_{0}I}{\pi }$
2. 
3. $\frac{7{\mu }_{0}I}{2R}$
4. 0

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

1. Zero, Zero 
2. -$\stackrel{\rightharpoonup }{\mathrm{F}}$ and Zero
3. $\stackrel{\rightharpoonup }{\mathrm{F}}$ and -$\stackrel{\rightharpoonup }{\mathrm{F}}$
4. $\stackrel{\rightharpoonup }{\mathrm{F}}$ 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 the north with a speed v₀, it moves with initial acceleration 3a₀, towards east. The electric and magnetic fields in the room are
1. $\frac{{\mathrm{Ma}}_0}{\mathrm{e}}\text{\hspace{0.17em}west,\hspace{0.17em}}\frac{2{\mathrm{Ma}}_0}{{\mathrm{ev}}_0}<mspace\; width="1em"></mspace>\mathrm{up}$
2. $\frac{{\mathrm{Ma}}_0}{\mathrm{e}}\text{\hspace{0.17em}west,\hspace{0.17em}}\frac{2{\mathrm{Ma}}_0}{{\mathrm{ev}}_0}<mspace\; width="1em"></mspace>\mathrm{down}$
3. $\frac{{\mathrm{Ma}}_0}{\mathrm{e}}\text{\hspace{0.17em}east,\hspace{0.17em}}\frac{2{\mathrm{Ma}}_0}{{\mathrm{ev}}_0}<mspace\; width="1em"></mspace>\mathrm{up}$
4. $\frac{{\mathrm{Ma}}_0}{\mathrm{e}}\text{\hspace{0.17em}east,\hspace{0.17em}}\frac{3{\mathrm{Ma}}_0}{{\mathrm{ev}}_0}<mspace\; width="1em"></mspace>\mathrm{down}$

If the current in an AC circuit is given as $\mathrm{i}=\left(5\mathrm{A}\right)\sin (\mathrm{\omega t}-\frac{\mathrm{\pi }}{3})$ when an emf
e=(200V) sin $\mathrm{\omega }$t is applied across the circuit. The circuit having component only
1. L and C
2. L and R
3. C and R
4. None of these

A step down transformer is employed to reduce the main supply of AC from 220 to 11V . If the primary coil draws a current of 5A and the secondary supplies a current to 90A, then efficiency of the transformer is
1. 10 %
2. 95 %
3. 90 %
4. 80 %

At resonance, the value of the power factor of the circuit is
1. 1
2. Zero
3. Between zero and 1
4. More than 1

If the planes of two identical concentric coils are perpendicular and the magnetic moment of each coil is M, then the resultant magnetic moment of the two coil system is
1. M
2. $\sqrt{2}$M
3. 3M
4. 2M

A voltmeter has a resistance G and it can measure a maximum voltage of V. To convert it into a voltmeter of range nV, the volume of resistance required is
1. (n-1) G in series
2. (n-1)G in parallel
3. $\frac{\mathrm{G}}{\mathrm{n}<mspace\; width="1em"></mspace>-<mspace\; width="1em"></mspace>1}$ in parallel
4. $\frac{\mathrm{G}}{\mathrm{n}<mspace\; width="1em"></mspace>-<mspace\; width="1em"></mspace>1}$ in series
 

A rod of length $\mathcal{l}$ rotates with uniform angular velocity $\mathrm{\omega }$ about an axis passing through its one end and perpendicular to its length. If a uniform magnetic field exists perpendicular to the axis of rotation, then induced emf across the two ends of the rod is
(1) $\frac{1}{2}$Bw$\mathcal{l}$²
(2) Bw$\mathcal{l}$²
(3) 2Bw$\mathcal{l}$²
(4) Zero

If a magnet is suspended at an angle of 30° to the magnetic meridian, the dip needle makes an angle of 45° with the horizontal. The value of the red dip angle at that place is
1. ${\tan }^{-1}\frac{\sqrt{3}}{2}$
2. ${\tan }^{-1}1$
3. ${\tan }^{-1}\frac{1}{2}$
4. ${\tan }^{-1}\left(\frac{2}{\sqrt{3}}\right)$

Soft iron is used to manufacture electromagnets because their
1. Magnetic saturation limit is high and coercivity is small
2. Retentivity is high
3. Coercivity is high
4. Area of the hysteresis loop is large

Two small bar magnets are placed in the air at a distance r apart. The magnetic force between them is proportional to 
1. r²
2. r^-2
3. r^-3
4. r^-4

The vertical component of the earth magnetic field is zero at
1. Magnetic poles
2. Magnetic equator
3. Geographic oles
4. Geographic equator

A resistance of 20 ohms is connected to a source of an alternating potential V = 220 sin(100 $\mathrm{\pi }$t). The time taken by the current to change from its peak value to r.m.s value is
1. 0.2 sec
2. 0.25 sec
3. 25 x 10^-3 sec
4. 2.5x 10^-3 sec