Question Bank for 12th Class Physics Magnetic Effects of Current / करंट का चुंबकीय प्रभाव Case Based (MCQs) - Moving Charges and Magnetism

The basic feature of a Banrbidge mass spectrometer is illustrated in figure. A particle carrying a charge +q is first sent through a velocity selector and comes out with velocity v = E/B.

The applied electric and magnetic field satisfy the relation E = vB so that the trajectory of the particle is a straight line.

Upon entering a regin where a second magnetic field \[{{\overrightarrow{B}}_{0}}\] pointing into the page has been applied, the particle will move in a circular path with radius r and eventually strike the photographic plate.

In mass spectrometer, the ions are sorted out in which of the following ways?

A)

By accelerating them through electric field

B)

By accelerating them through magnetic field

C)

By accelerating them through electric and magnetic field

D)

By applying a high voltage.

View Solution

2)

Radius of particle in second magnetic field \[{{B}_{0}}\] is

A)

\[\frac{2mv}{q{{E}_{0}}}\]

B)

\[\frac{mv}{q{{E}_{0}}}\]

C)

\[\frac{mv}{q{{B}_{0}}}\]

D)

\[\frac{2m{{E}_{0}}v}{q{{B}_{0}}}\]

View Solution

3)

Which of the following will trace a circular trajectory with largest radius?

A)

Proton

B)

\[\alpha -particle\]

C)

Electron

D)

A particle with charge twice and mass thrice that of electron.

View Solution

4)

Mass of the particle in terms q, \[{{B}_{0}}\], r and E is

A)

\[\frac{qBr}{E}\]

B)

\[\frac{q{{B}_{0}}Br}{E}\]

C)

\[\frac{qBr}{E{{B}_{0}}}\]

D)

\[\frac{qBrE}{{{B}_{0}}}\]

View Solution

5)

The particle comes out of velocity selector along a straight line, because

A)

electric force is less than magnetic force

B)

electric force is greater than magnetic force

C)

electric and magnetic force balance each other

D)

cant'say.

View Solution

6)

Directions : (6-10)

Ampere's Circular Law

Ampere's law gives a method to calculate the magnetic field due to given current distribution. According to it, the circulation \[\oint{\overrightarrow{B}\,.\,}d\overrightarrow{l}\] of the resultant magnetic field along a closed plane curve is equal to \[{{\mu }_{0}}\] times the total current crossing the area bounded by teh closed curve provided the electric field inside the loop remains constant. Ampere's law is more useful under certain symmetrical conditions. Consider one such case of a long straight wire with circular cross-section (radius R) carrying current I uniformly distributed across this cross-section.

The magnetic field at a radial distance r from the centre of the wire in the region r > R, is

A)

\[\frac{{{\mu }_{0}}I}{2\pi r}\]

B)

\[\frac{\mu I}{2\pi r}\]

C)

\[\frac{\mu I{{R}^{2}}}{2\pi r}\]

D)

\[\frac{\mu I{{r}^{2}}}{2\pi R}\]

View Solution

7)

The magnetic field at a distance r in the region r < R is

A)

\[\frac{{{\mu }_{0}}I}{2r}\]

B)

\[\frac{\mu \,I\,{{r}^{2}}}{2\pi {{R}^{2}}}\]

C)

\[\frac{\mu \,I}{2\pi r}\]

D)

\[\frac{{{\mu }_{0}}I\,r}{2\pi {{R}^{2}}}\]

View Solution

8)

A long straight wire of a circular cross-section (radius a) carries a steady curent I and the current I is uniformly distributed across this cross-section. Which of the following plots represents the variation of magnitude of magnetic field B with distance r from the centre of the wire?

A)

B)

C)

D)

View Solution

9)

A long straight wire of radius R carries a steady current I. The current is uniformly distribution across its cross-section. The ratio of magnetic field at R/2 and 2R is

A)

\[\frac{1}{2}\]

B)

2

C)

\[\frac{1}{4}\]

D)

1

View Solution

10)

A direct current I flows along the length of an infinitely long straight thin walled pipe, then the magnetic field is

A)

uniform throughout the pipe but not zero

B)

zero only along the axis of the pipe

C)

zero at any point inside the pipe

D)

maximum at the centre and minimum at the edges.

View Solution

11)

Directions : (11-15)

Helical Motion

The path of a charged particle in magnetic field depends upon angle between velocity and magnetic field.

If velocity \[\overrightarrow{v}\] is at angle \[\theta \] to \[\overrightarrow{B}\] component of velocity parallel to magnetic field \[\left( v\,\sin \theta \right)\]reamains constant and component of velocity perpendicular to magnetic field (v sin\[\theta \]) is responsible for circular motion, thus the charge particle moves in a helical path.

The plane of the circle is perpendicular to the magnetic field and the axis of the helix is parallel to the magnetic field.

The charged particle moves along helical path touching the line parallel to the magnetic field passing through the starting point after each rotation.

Radius of circular path is \[r=\frac{mv\,\sin \theta }{qB}\]

Hence the resultant path of the charged particle will be a helix, with its axis along the direction of \[\overrightarrow{B}\] as shown in figure.

When a positively charged particle enters into a uniform magnetic field with uniform velocity, its trajectory can be (i) a straight line (ii) a circle (iii) a helix.

A)

(i) only

B)

(i) or (ii)

C)

(i) or (iii)

D)

any one of (i), (ii) and (iii).

View Solution

12)

Two charged particles A and B having the same charge, mass and speed enter into a magnetic field in such a way that the initial path of A makes an angle of \[30{}^\circ \]and that of B makes an angle \[90{}^\circ \]with the field. Then the trajectory of

A)

B will have smaller radius of curvature than that of A

B)

both will have the same curvature

C)

A will have smaller radius of curvature than that of B

D)

both will move along the direction of their original velocities.

View Solution

13)

An electron having momentum \[2\,.\,4\times {{10}^{-23}}\,kg\] enters a region of uniform magnetic field of \[0\,.\,15\,T\]. The field vector makes an angle of \[30{}^\circ \]with the initial velocity vector of the electron. The radius of the helical path of the electron in the field shall be

A)

2 mm

B)

1 mm

C)

\[\frac{\sqrt{3}}{2}mm\]

D)

\[0\,.\,5\,mm\]

View Solution

14)

The magnetic field in a certain region of space is given by \[\overrightarrow{B}=8\,.\,35\,\times {{10}^{-2}}\hat{i}\,T\]. A proton is shot into the field with velocity \[\overrightarrow{v}=\left( 2\times {{10}^{5}}\hat{i}+4\times {{10}^{5}}\hat{j} \right)\]m/s. The proton follows a helical path in the field. The distance moved by proton in the x-direction during the period of one revolution in the yz-plane will be

A)

\[0\centerdot 053m\]

B)

\[0\centerdot 136m\]

C)

\[0\centerdot 157m\]

D)

\[0\centerdot 236m\]

View Solution

15)

The frequency of revolution of the particle is

A)

\[\frac{m}{qB}\]

B)

\[\frac{qB}{2\pi m}\]

C)

\[\frac{2\pi R}{v\,\cos \theta }\]

D)

\[\frac{2\pi R}{v\,\sin \theta }\]

View Solution

16)

Directions : (16-20)

Motion of Charge in Magnetic Fields

An electron with speed \[{{v}_{0}}<<c\] moves in a circle of radius \[{{r}_{0}}\] in a uniform magnetic field. This electron is able to traverse a circular path as magnetic field is perpendicular to the velocity of the electron. A force acts on the particle perpendicular to both \[{{\overrightarrow{v}}_{0}}\] and \[{{\overrightarrow{B}}_{0}}\]. This force continuously deflects the particle sideways without changing its speed and the particle will move along a circle perpendicular to the field. The time required for one revolution of the electron is \[{{T}_{0}}\].

If the speed of the electron is now doubled to \[2\,{{v}_{0}}\], the radius of the circle will change to

A)

\[4{{r}_{0}}\]

B)

\[2{{r}_{0}}\]

C)

\[{{r}_{0}}\]

D)

\[{{r}_{0}}/2\]

View Solution

17)

If \[{{v}_{0}}=2{{v}_{0}}\] then the time required for one revolution of the electron will charged to

A)

\[4{{T}_{0}}\]

B)

\[2{{T}_{0}}\]

C)

\[{{T}_{0}}\]

D)

\[{{T}_{0}}/2\]

View Solution

18)

A charged particle is projected in a magnetic filed \[\overrightarrow{B}=\left( 2\hat{i}+4\hat{j} \right)\times {{10}^{2}}T\]. The acceleration of the particle is found to be \[\overrightarrow{a}=\left( x\hat{i}+2\hat{j} \right)m{{s}^{-2}}\]. Find the value of x.

A)

\[4\,m\,{{s}^{-2}}\]

B)

\[-\,4\,m\,{{s}^{-2}}\]

C)

\[-2\,m\,{{s}^{-2}}\]

D)

\[2\,m\,{{s}^{-2}}\]

View Solution

19)

If the given electron has a velocity not perpendicular to B, then trajectory of the electron is

A)

straight line

B)

circular

C)

helical

D)

zig-zag

View Solution

20)

If this electron of charge (e) is moving parallel to uniform magnetic field with constant velocity v, the force acting on the electron is

A)

Bev

B)

\[\frac{Be}{v}\]

C)

\[\frac{B}{ev}\]

D)

zero

View Solution

21)

Directions : (21-25)

Torque on a Rectangular Loop Placed in Uniform Magnetic Field

When a rectangular loop PQRS of sides 'a' and 'b' carrying current I is placed in uniform magnetic field \[\overrightarrow{B}\], such that area vector \[\overrightarrow{A}\] makes an anlge \[\theta \] with direction of magnetic field, then forces on the arms QR and SP of loop are equal, opposite and collinear, there by perfectly cancel each other, whereas forces on the arms PQ and RS of loop are equal andopposite but not collinear, they give rise to torque on the loop.

Force on side PQ or RS of loop is F = Ib \[\sin \,90{}^\circ =Ib\,B\] and perpendicular distance between two non-collinear forces is \[{{r}_{\bot }}=a\,\sin \theta \]

So, torque on the loop, \[\tau =I\,\,AB\,\sin \theta \]

In vector form torque, \[\overrightarrow{\tau }=\overrightarrow{M}\times \overrightarrow{B}\]

where \[\overrightarrow{M}\times \,NI\,\overrightarrow{A}\] is called magnetic dipole moment of current loop and is directed in direction of area vector \[\overrightarrow{A}\] i-e., normal to the plane of loop.

A circular loop of area \[1\,c{{m}^{2}}\], carrying a current of 10 A is placed in a magnetic field of \[0\,.\,1\] T perpendicular to the plane of the loop. The torque on the loop due to the magnetic field is

A)

zero

B)

\[{{10}^{-4}}N\,m\]

C)

\[{{10}^{-2}}\,\,N\,m\]

D)

1 N m

View Solution

22)

Ralation between magnetic moment and angular velocity is

A)

\[M\propto \omega \]

B)

\[M\propto {{\omega }^{2}}\]

C)

\[M\propto \sqrt{\omega }\]

D)

none of these

View Solution

23)

A current loop in a magnetic field

A)

can be in equilibrium in two orientations, both the equilibrium states are unstable

B)

can be in equilibrium in two orientations, one stable while the other is unstable

C)

expereiences a torque whether (he field is uniform or non uniform in all orientations

D)

can be in equilibrium in one orientation.

View Solution

24)

The magnetic moment of a current I carrying circular coil of radius r and number of turns N varies as

A)

\[\frac{1}{{{r}^{2}}}\]

B)

\[\frac{1}{r}\]

C)

r

D)

\[{{r}^{2}}\]

View Solution

25)

A rectangular coil carrying current is placed in a non-uniform magnetic field. On that coil the total

A)

force is non-zero

B)

force is zero

C)

torque is zero

D)

none of these

View Solution

26)

Directions : (26-30)

Biot - Savart Low

A magnetic field can be produced by moving, charges or electric currents. The basic equation governing the magnetic field due to a current distribution is the Biot-Savart Law.

Finding the magnetic field resulting from a current distribution involves the vector product, and is inherently a calculas problem when the distance from the current to the field point is continuously changing.

According to the law, the magnetic field at a point due to a current element of length \[d\,\overrightarrow{l}\] carrying current I, at a distance r from the element is \[dB=\frac{{{\mu }_{0}}}{4\pi }\frac{I\left( d\overrightarrow{l}\times \overrightarrow{r} \right)}{{{r}^{3}}}\].

Biot-Savan law has certain similartities as well as difference with Coloumb's law for electrostatic field e.g., there is an angle dependence on Biot-Savart law which is not present in electrostatic case.

The direction of magnetic field \[d\overrightarrow{B}\] due to a current element \[d\overrightarrow{l}\] at a point of distance \[\overrightarrow{r}\] from it, when a current I passes through a long conductor is in the direction

A)

of position vector \[\overrightarrow{r}\] of the point

B)

of current element \[d\overrightarrow{l}\]

C)

perpendicular to both \[d\overrightarrow{l}\]and \[\overrightarrow{r}\]

D)

perpendicular to dl only

View Solution

27)

The magnetic field due to a current in a straight wire segment of length L at a point on its perpendicular bisector at a distance r (r > > L)

A)

decreases as \[\frac{1}{r}\]

B)

decreases as\[\frac{1}{{{r}^{2}}}\]

C)

decreases as\[\frac{1}{{{r}^{3}}}\]

D)

approaches a finite limit as \[r\to \infty \]

View Solution

28)

Two long straight wires are set parallel to each other.

Each carries a current i in the same direction and the separation between them is 2r. The instensity of the magnetic field midway between them is

A)

\[{{\mu }_{0}}i/r\]

B)

\[4{{\mu }_{0}}i/r\]

C)

zero

D)

\[{{\mu }_{0}}i/4r\]

View Solution

29)

A long straight wire carries a current along the z-axis for any two points in the x - y plane. Which of the following is always false ?

A)

The magnetic field are equal

B)

The directions of the magnetic field are the same

C)

The magnitudes of the magnetic field are equal

D)

The field at one point is opposite to that at the other point

View Solution

30)

Biot-Savart law can be expressed alternatively as

A)

Coulomb's Law

B)

Ampere's circuital law

C)

Ohm's Law

D)

Gauss' Law

View Solution

31)

Directions : (31-35)

Moving Coil Galvanometer

Moving coil galvanometer operates on Permanent Magne Moving Coil (PMMC) mechanism and was designed by the scientist D'arsonval.

Moving coil galvanometers are two types

(i) Suspended coil

(ii) Pivoted coil type or tangent galvanometer.

Its working is based on the fact that when a current carrying coil is placed ina magnetic field, it experiences a torque. This torque tends to rotate the coil about its axis of suspension in such a way that the magnetic field passing through the coil is maximum.

A moving coil galvanometer is instrument which

A)

is used to measure emf

B)

is used to measure potential difference

C)

is used to measure resistance

D)

is a deflection instrument which gives a deflection when a current flows through its coil

View Solution

32)

To make the field radial in a moving coil galvanometer

A)

number of turns of coil is kept small

B)

magnet is taken in the form of horse-shoe

C)

poles are of very strong magnets

D)

poles are cylinderically cut

View Solution

33)

The deflection in a moving coil galvanometer is

A)

directly proportional to torsional constant of spring

B)

directly proportional to the number of turns in the coil

C)

inversely proportional to the area of the coil

D)

inversely proportional to the current in the coil

View Solution

34)

In a moving coil galvanometer, having a coil of N-turns of area A and carrying current I is placed in a radial field of strength B. Th torque acting on the coil is

A)

\[N{{A}^{2}}{{B}^{2}}I\]

B)

\[NAB{{I}^{2}}\]

C)

\[{{N}^{2}}ABI\]

D)

NABI

View Solution

35)

The increase the current sensitivity of a moving coil galvanometer, we should decrease

A)

strength of magnet

B)

torsional constant of spring

C)

number of turns of coil

D)

area of coil

View Solution

36)

Directions : (36-40)

Conversion of Galvanometer to Voltmeter

A galvanometer can be converted into voltmeter of given range by connecting a suitable resistance \[{{R}_{s}}\] in series with the galvanometer, whose value is given by

\[{{R}_{s}}=\frac{V}{{{I}_{g}}}-G\]

where V is the voltage to be measured, \[{{I}_{g}}\] is the current for full scale deflection of galvanometer and G is the resistance of galvanometer.

Series resistor \[\left( {{R}_{s}} \right)\]increases range of voltmeter and the effective resistane of galvanometer. It also protects the galvanometer from damage due to large current.

Voltmeter is a high resistance instrument and it is always connected in parallel with the circuit element across which potential difference is to be measured. An ideal voltmeter has infinite resistance.

In order to increase the range of voltmeter n times the value of resistance to be connected in series with galvanometer is \[{{R}_{s}}=\left( n-1 \right)G\].

10 mA current can pass through a galvanometer of resistance\[25\Omega \]. What resistanfe in series should be connected through it, so that is it converted into a voltmeter of 100 ?

A)

\[0\centerdot 975\Omega \]

B)

\[99\centerdot 75\Omega \]

C)

\[975\Omega \]

D)

\[99\,75\,\Omega \]

View Solution

37)

There are 3 voltmeter A, B, C having the same range but their resistance are \[15,000\,\Omega \], \[10,\,000\,\Omega \] and \[5,000\,\Omega \] respectively. The best voltmeter amongst them is the one whose resistance is

A)

\[5,000\,\Omega \]

B)

\[10,000\,\Omega \]

C)

\[15,\,000\,\Omega \]

D)

all are equally good

View Solution

38)

A milliammeter of range 0 to 25 mA and resistance of \[10\,\Omega \] is 10 be convened into a voltmeter with a range of 0 to 25 V. The resistance that should be connected in series will be

A)

\[930\,\Omega \]

B)

\[960\,\Omega \]

C)

\[990\,\Omega \]

D)

\[1010\,\Omega \]

View Solution

39)

To converted a moving coil galvanometer (MCG) into a voltmeter

A)

a high resistance R is connected in parallel with MCG

B)

a low resistance R is connected in parallel with MCG

C)

a low resistance R is connected in series with MCG

D)

a high resistance R is connected in series with MCG

View Solution

40)

The resistance of an ideal voltmeter is

A)

zero

B)

low

C)

high

D)

infinity

View Solution

41)

Directions : (41-45)

Motion of Charged Particle Inside Magnetic Filed

A charged particle moving in a magnetic field experiences a force that is proportional to the strength of the magnetic field, the component of the velocity that is perpendicular to the magnetic field and the charge of the particle.

This force is given by \[\overrightarrow{F}=q\left( \overrightarrow{v}\times \overrightarrow{B} \right)\] where q is the electric charge of the particle, v is the instantaneous velocity of the particle, and B is the magnetic field (in tesla).

The direction of force is determined by the rules of cross product of two vectors.

Force is perpendicular to both velocity and magngetic field.

Its directin is same as \[\overrightarrow{v}\times \overrightarrow{B}\] if q is positive and opposite of \[\overrightarrow{v}\times \overrightarrow{B}\] if q is negative.

The force is always perpendicular to both the velocity of the particle and the magnetic field that created it. Because the magnetic force is always perpendicular to the motion, the magnetic field can do not work on an isolated charge. It can only do work indirectly, via the electric field generated by a changing magnetic field.

When a magnetic field is applid on a stationary electron, it

A)

remains stationary

B)

spins about its own axis

C)

moves in the direction of the field

D)

moves perpendicular to the direction of the field.

View Solution

42)

A proton is projected with a uniform velocity v along the axis of a current carrying solenoid, then

A)

the proton will be accelerated along the axis

B)

the proton path will be circular about the axis

C)

the proton moves along helical path

D)

the proton will continue to move with velocity v along the axis.

View Solution

43)

A charged particle experiences magnetic force in the presence of magnetic field. Which of the following statement is correct?

A)

The particle is stationary and magnetic field is perpendicular.

B)

The particle is moving and magnetic field is perpendicular to the velocity.

C)

The particle is stationary and magnetic field is parallel.

D)

The particle is moving and magnetic field is parallel to velocity.

View Solution

44)

A charge q moves with a velocity \[2\,m\,{{s}^{-1}}\] along x-axis in a uniform magnetic field \[\overrightarrow{B}=\left( \hat{i}+2\hat{j}+3\hat{k} \right)\] T, then charge will experience a force

A)

in z-y plane

B)

along -y axis

C)

along +z axis

D)

along -z axis

View Solution

45)

Moving charge will produe

A)

electric field only

B)

magnetic field only

C)

both electric and magnetic field

D)

none of these

View Solution

46)

Directions : (46-50)

Magnetic Field Due to solenoid

A solenoid is a long coil of wire tightly wound in the helical form. Solenoid consists of closely stacked rings electrically insulated from each other wrapped around a non-conducting cylinder. Figure below shows the magnetic field lines of a solenoid carrying a steady current I. We see that if the turns are closely spaced, the resulting magnetic field inside the solenoid becomes fairly uniformly, provided that the length of the solenoid is much greater than its diameter. For an "ideal" solenoid, which is infinitely long with turns tightly packed, the magnetic field inside the solenoid is uniform and parallel to the axis, and vanishes outside the solenoid.

A long solenoid has 800 turns per metre length of solenoid. A current of \[1\centerdot 6A\] flows through it. The magnetic induction at the end of the solenoid on its axis is

A)

\[16\times {{10}^{-4}}\,T\]

B)

\[8\times {{10}^{-4}}\,T\]

C)

\[32\,\times {{10}^{-4}}\,T\]

D)

\[4\times \,{{10}^{-4}}T\]

View Solution

47)

Choose the correct statement in the following:

A)

The magnetic field inside the solenoid is less than that of outside

B)

The magnetic field inside an ideal solenoid is not at all uniform

C)

The magnetic field at the cenre, inside an ideal solenoid is almost twice that at the ends

D)

The magnetic field at the centre, inside an ideal solenoid is almost half of that at the ends

View Solution

48)

The magnetic field [B] inside a long solenoid having n turns per unit length and carrying current I when iron core is kept in it is (\[{{\mu }_{0}}\]= permeability of vacuum, \[\chi \] = magnetic susceptibility)

A)

\[{{\mu }_{0}}nI\left( 1-\chi \right)\]

B)

\[{{\mu }_{0}}nI\chi \]

C)

\[{{\mu }_{0}}n{{I}^{2}}\left( 1+\chi \right)\]

D)

\[{{\mu }_{0}}nI\left( 1+\chi \right)\]

View Solution

49)

A solenoid of length l and having n turns carries a current I is an anticlockwise direction. The magnetic field is

A)

\[{{\mu }_{0}}nI\]

B)

\[{{\mu }_{0}}\frac{nI}{{{l}^{2}}}\]

C)

along the axis of solenoid

D)

perpendicular to the axis of coil

View Solution

50)

The magnitude of the magentic field inside a long solenoid is increased by

A)

decreasing its radius

B)

decreasing the curent through it

C)

increasing its area of cross-section

D)

introducing a medium of higher permeability

View Solution

12th Class Physics Magnetic Effects of Current / करंट का चुंबकीय प्रभाव Question Bank

done Case Based (MCQs) - Moving Charges and Magnetism Total Questions - 50

Study Package

Case Based (MCQs) - Moving Charges and Magnetism

Case Based (MCQs) - Moving Charges and Magnetism Total Questions - 50