Problem 5: A horizontal straight wire 10 m long extending from east to west is falling with a speed of 5 m/sec at right angle to the horizontal component of the earth’s magnetic field of 0.3 * 10-4 Wb/m2. (a) What is the instantaneous emf induced in the wire? (b) What is the direction of emf? (c) Which end of the wire is at higher potential?

#### Solution

Given data
Length of the wire = L = 10 m,
speed of the wire = v = 5 m/sec,
Magnetic field = 03 × 10-4 Wb/m2,
Angle of B and L = 90o
Required
Instantaneous emf=?
Direction of emf =?
Electric polarity of the wire =?

Theory

The earth’s magnetic field lines are approximately along the North-South direction on the earth. So if the wire in the problem extends from West to East, the horizontal component of the magnetic lines of force would be at right angle to the wire.

(a) Put the values in the formula F=LvB to get the magnitude of induced emf. (b) The constant magnetic field is from South to North. The conductor is moving downward. Apply the Fleming’s RHR, the direction of induced emf is from West to East.

(c) West side must be at higher potential by noting the direction of the current by Fleming RHR.