Moving Charges and Magnetism

A square loop ABCD carrying a current i, is placed near and coplanar with a long straight conductor XY carrying a current I, the net force on the loop will be [figure]

1. 2 0 IiL3
2. 0 IiL2
3. 2 0 Ii3
4. 0 Ii2

A long wire carrying a steady current is bent into a circular loop of one turn. The magnetic field at the centre of the loop is B. It is then bent into a circular coil of n turns. The magnetic field at the centre of this coil of n turns will be

1. nB
2. n2B
3. 2nB
4. 2n2B

An electron is moving in a circular path under the influence of a transverse magnetic field of 3.57 10-2 T. If the value of e/m is 1.76 1011 C kg-1, the frequency of revolution of the electron is

1. 1 GHz
2. 100 MHz
3. 62.8 MHz
4. 6.28 MHz

A circuit contains an ammeter, a battery of 30 V and a resistance 40.8 ohm all connected in series. If the ammeter has a coil of resistance 480 ohm and a shunt of 20 ohm, the reading in the ammeter will be

1. 2 A
2. 1 A
3. 0.5 A
4. 0.25 A

A proton and an alpha particle both enter a region of uniform magnetic field B, moving at right angles to the field B. If the radius of circular orbits for both the particles is equal and the kinetic energy acquired by proton is 1 MeV, the energy acquired by the alpha particle will be

1. 1.5 MeV
2. 1 MeV
3. 4 MeV
4. 0.5 MeV

A rectangular coil of length 0.12 m and width 0.1 m having 50 turns of wire is suspended vertically in a uniform magnetic field of strength 0.2 weber/m2. The coil carries a current of 2 A. If the plane of the coil is inclined at an angle of 30 with the direction of the field, the torque required to keep the coil in stable equilibrium will be

1. 0.24 Nm
2. 0.12 Nm
3. 0.15 Nm
4. 0.20 Nm

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. 0 n2 er
2. 0 n e2r
3. 0 n e2 r
4. Zero

A wire carrying current I has the shape shown in adjoining figure. [figure] Linear parts of the wire are very long and parallel to X-axis while semicircular portion of radius R is lying in Y-Z plane. Magnetic field at point O is

1. B = - 0 I4 R ( i + 2 k )
2. B = 0 I4 R ( i - 2 k )
3. B = 0 I4 R ( i + 2 k )
4. B = - 0 I4 R ( i - 2 k )

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. 1499 G
2. 499500 G
3. 1500 G
4. 500499 G

Two identical long conducting wires AOB and COD are placed at right angle to each other, with one above other such that O is their common point for the two. The wires carry I1 and I2 currents, respectively. Point P is lying at distance d from O along a direction perpendicular to the plane containing the wires. The magnetic field at the point P will be

1. 02 d ( I1I2 )
2. 02 d (I1 + I2 )
3. 02 d (I12 - I22 )
4. 02 d (I12 + I22 )1/2

When a proton is released from rest in a room, it starts with an initial acceleration a0 towards west. When it is projected towards north with a speed v0 it moves with an initial acceleration 3a0 towards west. The electric and magnetic fields in the room are

1. ma0e east, 3ma0ev0 up
2. ma0e east, 3ma0ev0 down
3. ma0e west, 2ma0ev0 up
4. ma0e west, 2ma0ev0 down

A current loop in a magnetic field

1. can be in equilibrium in two orientations, both the equilibrium states are unstable.
2. can be in equilibrium in two orientations, one stable while the other is unstable.
3. experiences a torque whether the field is uniform or non uniform in all orientations.
4. can be in equilibrium in one orientation.

A long straight wire carries a certain current and produces a magnetic field 2 10-4 Wb m-2 at a perpendicular distance of 5 cm from the wire. An electron situated at 5 cm from the wire moves with a velocity 107 m/s towards the wire along perpendicular to it. The force experienced by the electron will be (charge on electron 1.6 10-19 C)

1. 3.2 N
2. 3.2 10-16 N
3. 1.6 10-16 N
4. zero

A circular coil ABCD carrying a current 'i' is placed in a uniform magnetic field. If the magnetic force on the segment AB is F, the force on the remaining segment BCDA is [figure]

1. - F
2. 3 F
3. -3 F
4. F

A proton carrying 1 MeV kinetic energy is moving in a circular path of radius R in uniform magnetic field. What should be the energy of an -particle to describe a circle of same radius in the same field?

1. 2 MeV
2. 1 MeV
3. 0.5 MeV
4. 4 MeV

Two similar coils of radius R are lying concentrically with their planes at right angles to each other. The currents flowing in them are I and 2I, respectively. The resultant magnetic field induction at the centre will be

1. 5 0I2R
2. 5 0IR
3. 0I2R
4. 0IR

A millivoltmeter of 25 millivolt range is to be converted into an ammeter of 25 ampere range. The value (in ohm) of necessary shunt will be

1. 0.001
2. 0.01
3. 1
4. 0.05

An alternating electric field, of frequency , is applied across the dees (radius = R) of a cyclotron that is being used to accelerate protons (mass = m). The operating magnetic field (B) used in the cyclotron and the kinetic energy (K) of the proton beam, produced by it, are given by

1. B = m e and K = 2m 2 2R2
2. B = 2 e and K = m2 2
3. B = 2 e and K = 2m 2 2R2
4. B = m e and K = m2 2

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. G(S+G)
2. S2(S+G)
3. ( SGS+G )
4. G2(S+G)

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 at the centre of the ring is

1. 0 qf2 R
2. 0 qf2R
3. 0 q2fR
4. 0 q2 fR

A square loop, carrying a steady current I, is placed in a horizontal plane near a long straight conductor carrying a steady current I1 at a distance d from the conductor as shown in figure. The loop will experience [figure]

1. a net attractive force towards the conductor
2. a net repulsive force away from the conductor
3. a net torque acting upward perpendicular to the horizontal plane
4. a net torque acting downward normal to horizontal plane

A thermocouple of negligible resistance produces an e.m.f. of 40 / C in the linear range of temperature. A galvanometer of resistance 10 ohm whose sensitivity is 1 /division, is employed with the thermocouple. The smallest value of temperature difference that can be detected by the system will be

1. 1
2. 0.5
3. 0.1
4. 0.25

A current carrying closed loop in the form of a right angle isosceles triangle ABC is placed in uniform magnetic field acting along AB. If the magnetic force on the arm BC is F, the force on the arm AC is [figure]

1. - 2 F
2. - F
3. F
4. 2 F

A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an electron is projected in the region such that its velocity is pointed along the direction of fields, then the electron

1. will turn towards right of direction of motion
2. speed will decrease
3. speed will increase
4. will turn towards left of direction of motion

A current loop consists of two identical semicircular parts each of radius R, one lying in the x-y plane and the other in x-z plane. If the current in the loop is i. The resultant magnetic field due to the two semicircular parts at their common centre is

1. 0 i2 2R
2. 0 i2R
3. 0 i4R
4. 0 i 2R

A closely wound solenoid of 2000 turns and area of cross-section 1.5 10-4 m2 carries a current of 2.0 A. It is suspended through its centre and perpendicular to its length, allowing it to turn in a horizontal plane in a uniform magnetic field 5 10-2 tesla making an angle of 30 with the axis of the solenoid. The torque on the solenoid will be

1. 3 10-3 N m
2. 1.5 10-3 N m
3. 1.5 10-2 N m
4. 3 10-2 N m

A particle having a mass of 10-2 kg carries a charge of 5 10-8 C. The particle is given an initial horizontal velocity of 105 m s-1 in the presence of electric field E and magnetic field B. To keep the particle moving in a horizontal direction, it is necessary that Which one of the following pairs of statements is possible ?

1. A and C only
2. C and D only
3. B and C only
4. B and D only

Two identical bar magnets are fixed with their centers at a distance d apart. A stationary charge Q is placed at P in between the gap of the two magnets at a distance D from the centre O as shown in the figure [figure] The force on the charge Q is

1. zero
2. directed along OP
3. directed along PO
4. directed perpendicular to the plane of paper

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 at the center of the ring is

1. 0 q f2 R
2. 0 q f2R
3. 0 q2fR
4. 0 q2 f R

A galvanometer has a coil of resistance 100 ohm and gives a full scale deflection for 30 mA current. If it is to work as a voltmeter of 30 volt range, the resistance required to be added will be

1. 900
2. 1800
3. 500
4. 1000