Video Lecture
Theory For Notes Making
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Objective Assignment
Q.1
A conducting circular loop of radius r carries a constant current I. It is placed in a uniform magnetic field \vec{B} such that \vec{B} is perpendicular to the plane of the loop. The magnetic force acting on the loop is
(a) BIr (b) 2pIrB (c) zero (d) 2IrB
Ans. (c)
Q.2
A particle having mass m and charge q is attached to one end of a light rigid rod of length l. The rod is rotated at constant angular velocity about an axis normal to its length and passing through rod’s other free end. The ratio of the magnitude of the magnetic moment of the system and its angular momentum equals.
(a) \frac{q}{{2m}}
(b) \frac{1}{{m{{l}^{2}}}}
(c) \frac{q}{m}
(d) \frac{1}{{\pi m}}
Ans. (a)
Q.3
An insulating rod of length l carries a charge q distributed uniformly on it. The rod is pivoted at an end and is rotated at a frequency f about a fixed perpendicular axis. The magnetic moment of the system is
(a) zero
(b) \displaystyle \pi q f l2
(c) \frac{1}{2} \displaystyle \pi q f l2
(d) \frac{1}{3} \displaystyle \pi q f l2
Ans : (d)
4.
A circular coil of 30 turns and radius 8.0 cm carrying a current of 6.0 A is suspended vertically in a uniform magnetic field of magnitude 1.0 T. The field lines make an angle of 60° with the normal to the coil. Calculate the magnitude of counter torque that must be applied to prevent the coil from turning.
(a) 3.25 Nm
(b) 3.14 Nm
(c) 3.00Nm
(d) 3.50 Nm
Ans (b)
5.
A coil in the shape of an equilateral triangle of side 0.02 m is suspended from a vertex such that it is hanging in a vertical plane between the pole pieces of a permanent magnet producing a horizontal magnetic field of 5\times {{10}^{{-2}}}T. Find the couple acting on the coil. When a current of 0.1 ampere is passed through it and the magnetic field is parallel to its plane.
(a) 7.5\times {{10}^{{-7}}}\,N-m
(b) 8.00\times {{10}^{{-7}}}\,N-m
(c) 8.66\times {{10}^{{-7}}}\,N-m
(d) 9.0\times {{10}^{{-7}}}\,N-m
Ans (c)
6.
A circular coil of 200 turns, radius 5 cm carries a current of 2.5 A. It is suspended vertically in uniform horizontal magnetic field of 0.25 T, with the plane of the coil making an angle of 60° with the field lines. Calculate the magnitude of ht torque that must be applied on it to prevent if from turning.
(a) 0.60 Nm
(b) 0.49 Nm
(c) 0.25 Nm
(d) 0.30 Nm
Ans (b)
Subjective Assignment
Q.1.
Define the term magnetic moment.
Q.2
A coil carrying current is suspended freely. If a magnetic field is suddenly applied around it in which position will the coil come to rest ?
Q.3
In an orbit of hydrogen of radius 0.5Ao an electron is moving with a speed of 107 m/sec .find the magnetic moment of the orbit and calculate the maximum torque acting on it if the earth’s magnetic field at the place is 100G
Q.4
A circular coil of wire, 0.05 m radius, having 40 turns, lies in a horizontal plane.It carries a current of 5 A, in anti-clockwise direction, as seen from above. The coil is placed in a magnetic field of 1.2 T, directed to right. Calculate the magnetic moment and torque on the coil
Q.5
Find the torque acting on the coil in the following diagram.
Q..6
A uniform magnetic field of 3000G is existing along +ve z direction.A rectangular loop of side 10cm and 5cm carrying a current of 12A is placed in that region in different positions as shown in the diagram.Find the torque and the force acting on the loop in all these positions, and the position corresponds to stable equilibrium.
Q.7.
A current of 7A is flowing in a plane circular coil of radius 1 cm having no. of turns 100. The coil is placed in a uniform magnetic field of 0.2 wh/m2. If the coil is free to rotate which orientation would correspond to (i) stable equilibrium (ii) unstable equilibrium ? Calculate P.E. in two cases?
Q.8.
A circular coil is placed in a uniform magnetic field of strength 0.10 T normal to the plane of the coil. If the current in the coil is 5.0 A, find
(i) total torque on the coil
(ii) total force on the coil
(iii) average force on each electron in the coil due to the magnetic field (the coil is made of copper wire of cross-sectional area 10-5 m2 and the free electron density in copper is 1029 rn-3). [Ans. 0.5×10’24N]