(c) Find an expression for the magnitude of the induced current in the loop at time t, in terms of the symbols above and appropriate constants. What is the maximum magnitude of the induced current in mA and how many times does this occur per second?
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So using I=V/R
I=AB w sin wt/R
AB w sin wt is the derived equation for the induced EMF.
Is this on the right track?
Yes, you are on the right track. To find the magnitude of the induced current in the loop at time t, you can use Ohm's Law: I = V/R.
In this case, the induced electromotive force (EMF) is given by the equation EMF = ABωsin(ωt), where A is the amplitude of the magnetic field, B is the magnetic field strength, ω is the angular frequency, and t is the time.
Since the induced EMF is equal to the product of the magnetic field strength and the rate of change of magnetic flux through the loop, we can use Faraday's Law to relate the induced EMF to the magnetic field strength and angular frequency:
EMF = -d(Φ)/dt
where d(Φ) represents the change in magnetic flux through the loop over time. The negative sign indicates that the induced current flows in such a direction as to oppose the change in magnetic flux.
Now, let's find the expression for the induced current in terms of the symbols given and appropriate constants. We can rewrite Ohm's Law for this specific case as follows:
I = (ABωsin(ωt))/R
This equation represents the magnitude of the induced current at any given time t.
To determine the maximum magnitude of the induced current, we need to find the maximum value of the sine function. The maximum value of sin(ωt) is 1, so the maximum magnitude of the induced current (in amperes) is:
I_max = (ABω)/R
To convert this value to milliamperes (mA), we multiply it by 1000:
I_max_mA = (1000 * ABω)/R
To find the number of times the maximum magnitude of the induced current occurs per second, we need to determine the frequency of the oscillation. The frequency (f) is the reciprocal of the period (T), which is the time it takes for one complete cycle. The period is given by:
T = 2π/ω
Thus, the frequency is:
f = 1/T = ω/2π
Therefore, the maximum magnitude of the induced current occurs f times per second:
Number of times per second = f = ω/2π
Remember to substitute the appropriate values for A, B, ω, and R into the equations to calculate specific values for the magnitude of the induced current and the number of times it occurs per second.