To find the current induced in the rectangular coil due to the changing magnetic field, you can use Faraday's law of electromagnetic induction. According to Faraday's law, the induced electromotive force (EMF) in a coil is equal to the rate of change of magnetic flux through the coil. The formula for the induced EMF is:
EMF = -N * dΦ/dt
Where:
EMF is the induced electromotive force (in volts).
N is the number of turns in the coil (20 turns in this case).
dΦ/dt is the rate of change of magnetic flux (in webers per second, which is equivalent to teslas per second in this context).
First, let's calculate the rate of change of magnetic flux (dΦ/dt). Given that the magnetic field changes at a rate of 1000 teslas per second and the area of the coil is 25 sq. cm (which can be converted to square meters), you can calculate dΦ/dt as follows:
dΦ/dt = B * A * cos(θ) / dt
Where:
B is the magnetic field strength (1000 teslas).
A is the area of the coil (25 sq. cm = 0.0025 square meters).
θ is the angle between the magnetic field and the normal to the coil, which is 90 degrees in this case (perpendicular).
dt is the change in time (1 second).
Now, plug in the values:
dΦ/dt = (1000 teslas) * (0.0025 square meters) * cos(90 degrees) / 1 second
dΦ/dt = 2.5 webers per second
Now, you can use Faraday's law to calculate the induced EMF:
EMF = -N * dΦ/dt
EMF = -(20 turns) * (2.5 webers per second)
EMF = -50 volts
Since the induced EMF in the coil is -50 volts, and the resistance of the coil is 100 ohms, you can use Ohm's law (V = IR) to find the current (I):
I = EMF / R
I = (-50 volts) / (100 ohms)
I = -0.5 ampere
The negative sign indicates that the current direction is opposite to the direction of the induced EMF. So, the correct answer is:
C. 0.5 ampere
