Important questions based on NCERT syllabus for Chapter 6 - Electromagnetic Induction:
Question-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.
r = 1 m
ω = 400 rad / s
B = 0.5 T
ϕ’ = B.A.cosθ = 0.5 × 3.41 × 1 = 1.571 Wb
ϕ’’ = B.A.cos180o = 0.5 × 3.41 × 1 = ‒1.571 Wb
ω = 400 or f = 400/(2 × 3.14) = 63.66 / s
Therefore E = [1.571 – (‒ 1.571)] / 0.0314
Or E = 100 V.
Question-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?
(b) What is the direction of the emf?
(c) Which end of the wire is at the higher electrical potential?
l = 10 m
v = 5 m / s
H = 0.3x10-4 Wb m2
(a) Einst = Blv = (0.00003) × (10) × (5) = 1.5 × 10‒3 V
(b) West to east.
(c) Eastern end.
Question-3: A pair of adjacent coils has a mutual inductance of 1.5 H. If the current in one coil changes from 0 to 20 A in 0.5 s, what is the change of flux linkage with the other coil?
M = 1.5 H
dI = 20 A
dt = 0.5 s
d(Nϕ) / dt = d(MI) / dt
Putting the values
d(Nϕ) = 30 webers.