A straight horizontal 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 ｘ10⁻⁴ Wb m⁻² 
(a) what is the instantaneous value of the e.m.f. induced in the wire? 
(b)What is the direction of the e.m.f.? 
(c)Which end of the wire is at the higher electrical potential? 

(Answer: 1.5 ｘ10⁻³ V)  



Data Given:

Length of the wire = L = 10 m

Falling speed = v = 5.0 m s⁻¹

Magnetic Field = B = 0.30 ｘ 10⁻⁴ T


To Find:

(a) Induced e.m.f. in the wire= Ɛ = ?

(b) Direction of the e.m.f.

(c) Higher Electrical Potential


Solution:

(a) Induced e.m.f. in the wire= Ɛ = ?

The equation for the motional e.m.f. is given by:

Ɛ = B l v

by putting values

Ɛ = 0.30 ｘ 10⁻⁴ T ｘ 10 m ｘ 5.0 m s⁻¹

Ɛ = 15 ｘ 10⁻⁴ V

or

Ɛ = 1.5 ｘ 10⁻³ V

or

Ɛ = 1.5 ｘ mV ------------Ans. (1)


(b) Direction of the e.m.f.

The direction the motional e.m.f. will be from west to east.


(c) Higher Electrical Potential:

Since the current flows from higher potential to lower potential. So in this case the western end of the wire will be at higher potential because the current flows from west to east.



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