Video Lecture
Theory For Notes Making
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Ut elit tellus, luctus nec ullamcorper mattis, pulvinar dapibus leo.
Objective Assignment
Q.1
A copper rod of length l is rotated about one end perpendicular to the uniform magnetic field B with constant angular velocity w. The induced emf between two ends is –
(a) \frac{3}{2}Bwl2
(b) Bwl2
(c) 2Bwl2
(d) \frac{1}{2}Bwl2
Ans : (d)
Q.2
The wire AB slides with velocity v and remains in contact with fixed rails. If the wire AB is replaced by a semicircular arc, the magnitude of induced current will
(a) increase
(b) remain the same
(c) decrease
(d) depends on the orientation of arc
Ans. (b)
Q.3
A rod of length l rotates with a uniform angular velocity w about its perpendicular bisector. A uniform magnetic field B exists parallel to the axis of the rotation. The potential difference between the two ends of the rod is
(a) zero
(b) \frac{1}{2}Bl{{\omega }^{2}}
(c) Bl{{\omega }^{2}}
(d) 2Bl{{\omega }^{2}}
Ans : (a)
Q.4
A rod AB moves with a uniform velocity v An a uniform magnetic field as shown in figure.
(a) The rod becomes electrically charged.
(b) The end A becomes positively charged
(c) The end B becomes positively charged.
(d) The rod becomes hot because of Joule heating. A
Ans. (b)
Q.5
A metal rod of length \vec{l} is moved with a constant velocity \vec{v} in a magnetic field \vec{B}. A potential difference appears across the two ends when
(a) \vec{v}||\vec{l}
(b) \vec{v}||\vec{B}
(c) \vec{l}||\vec{B}
(d) none of these
Ans: (d)
Subjective Assignment
Q.1
A 1.0 m long metallic rod is rotated with an angular frequency of 400 rad s–1 about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field of 0.5 T parallel to the axis exists everywhere. Calculate the emf developed between the centre and the ring.
Ans. 100V
Q.2
A horizontal straight wire 10 m long extending from east to west is falling with a speed of 5.0 m s–1, at right angles to the horizontal component of the earth’s magnetic field,
0.30 × 10–4 Wb m–2
(a) What is the instantaneous value of the emf induced in the wire?
Ans. \displaystyle 1.5\,\times \,{{10}^{{-3}}}\,V
(b) What is the direction of the emf?
Ans. West to East,
(c) Which end of the wire is at the higher electrical potential?
Ans. Eastern end
Q.3
A jet plane is travelling towards west at a speed of 1800 km/h. What is the voltage difference developed between the ends of the wing Electromagnetic Induction having a span of 25 m, if the Earth’s magnetic field at the location has a magnitude of 5 × 10–4 T and the dip angle is 30°.
Ans. \displaystyle \varepsilon \,=\,3.125\,V
Q.4
A rectangular wire loop of sides 8 cm and 2 cm with a small cut is moving out of a region of uniform magnetic field directed normal to the loop. If the loop is stationary but the current feeding the electromagnet that produces the magnetic field is gradually reduced so that the field decreases from its initial value of 0.3 T at the rate of 0.02 T s–1. If the cut is joined and the loop has a resistance of 1.6 Ω, how much power is dissipated by the loop as heat? What is the source of this power?
Ans. Power loss \displaystyle =\,6.4\,\times \,{{10}^{{-10}}}\,W
Q.5
A square loop of side 12 cm with its sides parallel to X and Y axes is moved with a velocity of 8 cm s–1 in the positive x-direction in an environment containing a magnetic field in the positive z-direction. The field is neither uniform in space nor constant in time. It has a gradient of 10 –3 T cm–1 along the negative x-direction (that is it increases by
10–3 T cm–1 as one moves in the negative x-direction), and it is decreasing in time at the rate of 10 –3 T s–1. Determine the direction and magnitude of the induced current in the loop if its resistance is 4.50 mΩ.
Ans. Induced current = \displaystyle 2.88\,\times \,{{10}^{{-2}}}\,A The direction of induced current is such as to increase the flux through the loop along positive z-direction.
Q.6
It is desired to measure the magnitude of field between the poles of a powerful loud speaker magnet. A small flat search coil of area 2 cm2 with 25 closely wound turns, is positioned normal to the field direction, and then quickly snatched out of the field region. Equivalently, one can give it a quick 90° turn to bring its plane parallel to the field direction). The total charge flown in the coil (measured by a ballistic galvanometer connected to coil) is 7.5 mC. The combined resistance of the coil and the galvanometer is 0.50 Ω. Estimate the field strength of magnet.
Ans. B = \displaystyle {{\phi }_{t}}/A\,=\,0.75\,T
Q.7
A jet plane is travelling west at 450 m/s. If the horizontal component of earth’s magnetic field at that place is \displaystyle 4\,\times \,{{10}^{{-4}}} T and the angle of dip is 30º, find the emf induced between the ends of wings having a span of 30 m.
Q.8
(a) \displaystyle |\varepsilon |\,=\,9.0\,mV
(b) Yes, when K is closed the excess charge is maintained by the continuous flow of current.
(d) Retarding force = \displaystyle |\varepsilon |\,=\,9.0\,mV
(e) Power expended by an external agent.
\displaystyle =75\,\times \,{{10}^{{-3}}}\,\times \,12\,\,\times \,{{10}^{{-2}}}=9.0\,\times \,{{10}^{{-3}}}\,W When K is open, no power is expended.
(f) \displaystyle {{I}^{2}}R\,=\,1\,\times \,1\,\times \,9\,\times \,{{10}^{{-3}}}\,=9.0\,\times \,{{10}^{{-3}}}\,W
(g) Zero
Q.9
Figure shows a metal rod PQ resting on the smooth rails AB and positioned between the poles of a permanent magnet. The rails, the rod, and the magnetic field are in three mutual perpendicular directions. A galvanometer G connects the rails through a switch K. Length of the rod = 15 cm, B = 0.50 T, resistance of the closed loop containing the rod = 9.0 mΩ. Assume the field to be uniform.
(a) Suppose K is open and the rod is moved with a speed of 12 cm s–1 in the direction shown. Give the polarity and magnitude of the induced emf.
(b) Is there an excess charge built up at the ends of the rods when K is open? What if K is closed?
(c) With K open and the rod moving uniformly, there is no net force on the electrons in the rod PQ even though they do experience magnetic force due to the motion of the rod. Explain.
(d) What is the retarding force on the rod when K is closed?
(e) How much power is required (by an external agent) to keep the rod moving at the same speed (=12 cm s–1) when K is closed? How much power is required when K is open?
(f) How much power is dissipated as heat in the closed circuit? What is the source of this power?
(g) What is the induced emf in the moving rod if the magnetic field is parallel to the rails instead of being perpendicular?
Q.10
A long, straight wire has a constant current I. A metal rod of length l moves at velocity v relative to the wire, as shown in figure. What is the potential difference between the ends of the rod?
Ans :
\frac{{{{\mu }_{o}}Iv}}{{2\pi }}\,\ln \left| {\frac{{l\,+\,d}}{d}} \right|
Q.11
A long straight wire carrying a current I and a U-shaped conductor with sliding connector are located in the same plane as shown in the figure. The connector of length l and resistance R slides to the right with a constant velocity v. Find the current induced in the loop as a function of separation x between the connector and the straight wire.
Ans.
Iind = \frac{\alpha }{x}, where x =1/2 µolvI/pR
Q.12
In the given diagram, a 0.5 m long metal rod AC can slide on the wires LM and KN which are connected by a resistance of 3 W. The magnetic field, pointing into the paper, has magnitude 0.15 T. Calculate the force needed to move the rod with a constant speed of 2 m/s.
Ans. 16 p x 10-12 A, Anticlockwise.