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Multiple choice mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

An electron having kinetic energy T is moving in a circular orbit of radius R perpendicular to a uniform magnetic induction $\vec { \mathrm { B } }$  If kinetic energy is doubled and magnetic induction tripled, the radius will

  1. $\frac { 3 R } { 2 }$

  2. $ \frac{{\sqrt 2 }}{3}R$

  3. $\sqrt { \frac { 2 } { 9 } } R$

  4. $\sqrt { \frac { 4 } { 3 } } R$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

We know$,$

$R = \frac{{\sqrt {2mk} }}{{qB}}$
$R' = \frac{{\sqrt {2m2k} }}{{q\left( {3B} \right)}}$
$ = \frac{{\sqrt 2 }}{3}\frac{{\sqrt {2mk} }}{{qB}}$
$ = \frac{{\sqrt 2 }}{3}R$
Hence,
option $(B)$ is correct answer.

Multiple choice mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

When a current of 5 A flows in the primary coil then the flux linked with the secondary coil is 200 weber. The value of coefficient of mutual induction will be

  1. 1000 H

  2. 40 H

  3. 195 H

  4. 205 H
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Coefficient of mutual induction will be the ratio of the flux linked with the secondary coil and the current primary coil.


$ M = \dfrac{200}{5} = 40 H $ 

Multiple choice mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

A cylindrical magnet is kept along the axis of a circular coil. On rotating the magnet about its axis. the coil will have induced in it

  1. No current

  2. A current

  3. Only an e.m.f.

  4. Both an e.m.f. and a current
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Rotating a cylindrical magnet about its own axis does not change the magnetic flux linked with the stationary circular coil. According to Faraday's law, no flux change means no induced EMF and no induced current.

Multiple choice mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

A coil of insulating wire is connected to battery. If it is moved towards a galvanometer then its point gets deflected because

  1. the coil behaves like a magnet

  2. induced current is produced in the coil

  3. the number of turns in the galvanometer coil remains constant

  4. none of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Upon connecting to the battery , a current starts to flow in the insulated wire. This current induces a current in the galvanometer coil  due to mutual  inductance because of the flux linkages. This induced current causes a deflection in the galvanometer . 

Multiple choice mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

Two coils P and Q are lying parallels and very close to each other. Coil P is connected to an AC source whereas Q is connected to a sensitive galvanometer. On pressing key K

  1. small variations are observed in the galvanometer for applied 50 Hz voltage

  2. deflections in the galvanometer can be observed for applied voltage of 1 Hz to 2 Hz.

  3. no deflection in the galvanometer will be observed

  4. constant deflection will be observed in the galvanometer for 50 Hz supply voltage
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Upon connecting to the AC source , a current starts to flow in the coil P. This current induces a current in the galvanometer coil Q due to mutual  inductance because of the flux linkages. This induced current causes a deflection in the galvanometer.

Multiple choice mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

The value of mutual inductance can be increased by

  1. decreasing N

  2. increasing N

  3. winding the coil on wooden frame

  4. winding the coil on china clay
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$M = \mu N _1 N _2 \dfrac{ Area _{12}}{length _{12}} $


$ Area _{12} $ - area in common to both the coils where the flux links both of them together.
$length _{12}$ - length in common to both the coils where the flux links both of them together.
Therefore to increase the mutual inductance, the number of turns can be increased.  

Multiple choice mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

A long straight wire is placed along the axis of a circular ring of radius R. Then mutual inductance of this system is 

  1. $\frac{\mu _{0}R}{2}$

  2. $\frac{\mu _{0}\pi R}{2}$

  3. $\frac{\mu _{0}}{2}$

  4. 0
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A long straight wire placed along the axis of a circular ring produces a magnetic field that is parallel to the plane of the ring (or perpendicular to the area vector of the ring). Thus, the magnetic flux through the ring is zero, and the mutual inductance is zero.