Explain with the help of a well labelled
diagram, its working and obtain the
expression for the emf generated in the
coil?
Answers
Explanation:
(a) Principle:
It works on the principle of Faraday’s law of electromagnetic induction. Whenever a coil is rotated in a uniform magnetic field about an axis perpendicular to the field, the magnetic flux linked with coil changes and an induced emf is set up across its ends.
Working:
When the coil starts rotating with the arm AB moving up and the arm CD moving down, cutting the magnetic lines of force, then according to Fleming's right-hand rule and the induced current is set up in these arms along the direction of AB and CD. So an effective induced current flowing in the direction of ABCD is obtained.
If there are large number of turns in the coil, the current generated in each turn adds upto give a large quantity of current through the coil.
After half rotation of the coil, its arm CD starts moving up and AB moving down. As a result, the direction of the induced currents gets reversed in the coil in the direction of DCBA. Thus after every half rotation the polarity of the current in the respective arm changes. Such a current, which changes its direction after equal intervals of time, is called to get a direct current a split ring type commutator must be used in place of slip ring commutator.
emf induced in a coil
Consider a coil of N turns and area A being rotated at a constant angular velocity ω in a magnetic field of flux density B, its axis being perpendicular to the field.
When the normal to the coil is at an angle θ to the field, the flux through the coil is BAN cosθ = BAN cos(ω)t, since θ = ωt.
E=−
dt
dϕ
E=−
dt
d(BANcosθ)
E=BANωsin(ωt)
The maximum value of the e.m.f (E
o
) is when θ (= ωt) = 90o (that is, the coil is in the plane of the field as shown in Figure 2) and is given by
E
o
=BANω
B. We know that e = Blv
but tanθ=
B
H
B
v
B
v
=B
H
tanθ
e=B
v
lV
e=B
H
tanθlV
e=5×10
−4
(tan30
o
)(20)(500) Volt
so e = 2.88 volt
