Download Chapter 3.5— ELECTROMAGNETIC INDUCTION I

F.7 AL PHYSICS
ASSIGNMENT 4
Chapter 3.5— ELECTROMAGNETIC INDUCTION I
SOLUTIONS
1. (a) I. Faraday’s law :
The induced e.m.f. is directly proportional to the rate of change of flux linkage.
II. Lenz’s law :
The e.m.f. is induced in such a direction that it tends to oppose the flux change
causing it, and does oppose it if induced current flows.
(The minus sign means that the e.m.f. opposes the change of the flux.)
(b) (i) Free electrons inside the metal rod are deflected downwards towards the end Q by
the magnetic force while the rod is being moved to the right.
A p.d. is set up between P and Q with P at the higher potential.
At equilibrium, the magnetic force will be balanced by the electric force.
Hence, free electrons stop moving to the end Q and the p.d. between P and Q will
be derived as follows:
FE = FB
eE = Bev
E = Bv
P
V
= Bv
l
V = Blv
Q
(ii) The induced current flows from P to Q through the wire.
Hence, a magnetic force FB’ is set up to oppose the motion of the rod.
Thus, work should be done by the external agent to keep the rod moving in uniform
velocity such that Fext. = FB’
Hence, the mechanical work is converted into electrical energy and dissipated as
heat in the rod eventually. It is therefore consistent with the principle of
conservation of energy.
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(c) The flux through the coil increases when the magnet is approaching.
As seen from above, the induced current flows
anti-clockwisely to oppose the motion by Lenz's law.
Similarly, the flux through the coil decreases when the magnet is leaving.
As seen from above, the induced current flows clockwisely to oppose the motion by
Lenz's law.
The magnitude of induced current is directly proportional to the rate of change of
magnetic flux through the coil, i.e.,
I=

R

1 d
R dt
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