Name: Alternating Current - An Overview
Uploaded: 2019-07-19
Duration: 8 min 44 s
Description: This video elucidates what alternating current is and how it is different from direct current. It also depicts some alternating current functions graphically.

Question

What is motional emf, Deduce an expression for it from the following diagram. If $R$ be the resistance of the loop $PQRS$ at agiven instant, what will be induced current at that instant?

A straight conductor of length $0.1 m$ moves with a speed of $10 {ms}^{- 1}$ perpendicular to the magnetic field of induction $1 web / m^{2}$ . Calculate the induced e.m.f. State Len's law.

Accepted Answer

An emf induced by the motion of the conductor across the magnetic field is a motional electromotive force. The equation is given by

$E = - vLB$

For this expression, the velocity, field, and length are mutually perpendicular. The minus sign is associated with the Lenz's law.

Consider a straight conductor $PQ$ as shown in the figure, moving in the rectangular loop $10 {ms}^{- 1}$ a uniform and time-independent magnetic field $B$ perpendicular to the plane of the system. Let us suppose the motion of the rod to be uniform at a constant velocity of $v$ on a to frictionless surface. Thus, the rectangle $PQRS$ forms a closed circuit enclosing a varying area due to the motion of the rod $PQ$
The magnetic flux $ϕ_{B}$ enclosed by the loop $PQRS$ can be given as
$ϕ_{B} = Blx$ .

Where, $RQ = x and RS = l$ Since the conductor is moving, $x$ i s changing with time. Thus, the rate of change of flux $ϕ_{B}$ will induce an emf, which is given by:

$ε = - \frac{{dϕ}_{B}}{dt} = - \frac{d}{dt} (Blx) = - Bl \frac{dx}{dt} = - Blv$ ...............(A)

Where the speed of the conductor $PQ = v = \frac{dx}{dt}$ .

This is the expression of the motional emf due to the motion of a conductor in a magnetic field.

The current in the conductor is given by $I = \frac{E}{R} = \frac{Blv}{R}$

Given the length of the conductor $i = 0.1 m$ .

The speed of the conductor $v = 10 {ms}^{- 1}$

The magnetic field $0.1 m$ ,

The motional emf is $e = - Blv = - 1 \times 0.1 \times 10 = - 1 V$ .

Important Questions on Electromagnetic Induction

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