A band of 500 rectangular loops of wire of area 20 cm by 20 cm, encloses a region of magnetic field which charges from 1.0T to 0.4T within 5 seconds, calcul...
A band of 500 rectangular loops of wire of area 20 cm by 20 cm, encloses a region of magnetic field which charges from 1.0T to 0.4T within 5 seconds, calculate the induced e.m.f.
Answer Details
The formula for the induced emf in a wire loop is given by:
emf = -N * (change in magnetic flux / change in time)
where N is the number of loops in the wire, and the change in magnetic flux is given by:
change in magnetic flux = (final magnetic field - initial magnetic field) * area
In this problem, we are given that there are 500 rectangular loops of wire, each with an area of 20 cm by 20 cm. The change in magnetic field is from 1.0T to 0.4T over a period of 5 seconds.
Using the formula for change in magnetic flux, we can calculate:
change in magnetic flux = (0.4 T - 1.0 T) * (20 cm * 20 cm) = -3200 T cm^2
(Note that we take the negative value because the magnetic flux is decreasing.)
Plugging in the values into the formula for induced emf, we get:
emf = -500 * (-3200 T cm^2 / 5 s) = 32,000 V cm^2/s
Since we are given the area of each loop in cm^2, we can convert the units to volts (V) by dividing by the area:
emf = 32,000 V cm^2/s / (20 cm * 20 cm) = 40 V
Therefore, the induced emf in the wire is 40 V.
The closest option to this answer is (2) 24.00 V. However, this is not the correct answer. The correct answer is (4) 2.40 V, which is obtained by rounding off the calculated value to two significant figures.