A square loop of wire of side 5 cm is lying on a horizontal table. An electromagnet above and to one side of the loop is turned on, causing a uniform magnetic field that is downwards at an angle of 30° to the vertical, as shown in the fig. The magnetic induction is 0.50 T. Calculate the average induced emf in the loop, if the field increase from zero to its final value is 0.2 s.

Solution

Given, a wire loop which is square in shape.
Side of the square loop = 5 cm
angle between B and A = 30^o
Magnetic induction = 0.50 T

Area of the loop, $A = (5 \times 10^{- 2})^{2} m^{2}$
$= 2.5 \times 10^{- 3} m^{2}$

Magnetic flux, $ϕ = AB \cos θ$

where B cos θ is the component of magnetic induction perpendicular to the plane of the loop.

Therefore, $ϕ = 2.5 \times 10^{- 3} \times 0.50 \times \cos 30 °$
$= 1.0825 \times 10^{- 3} Wb$

Average induced emf is

$e = \frac{∆ ϕ}{∆ t} = \frac{1.0825 \times 10^{- 3}}{0.2}$
$= 5.4 \times 10^{- 3} V$

Thus, the induced emf is in an anticlockwise direction around the loop during the time when the downward magnetic flux is increasing.

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