Moving Charges and Magnetism · Question 47

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