A wire which moves with a speed of 4.6ms–1 is 17.0 long and has negligible resistance. The magnitude of the magnetic field is 0.25T and the resistance of the u- shaped conductor is 25.00 ohms at a given instance. Calculate the induced emf and the current flowing in the u– shaped conductor
To calculate the induced emf, we can use Faraday's law of electromagnetic induction:
emf = -N dΦ/dt
where:
emf is the induced electromotive force,
N is the number of turns of wire,
dΦ/dt is the rate of change of magnetic flux.
In this case, the wire has negligible resistance, so we can assume that all of the emf induced across the wire will appear as current in the circuit. Therefore, the induced emf is equal to the voltage across the resistance:
emf = V = IR
where:
I is the current flowing through the wire, and
R is the resistance of the u-shaped conductor.
We can rearrange the first equation to solve for the rate of change of magnetic flux:
dΦ/dt = -(emf / N)
Given:
Speed of the wire (v) = 4.6 m/s
Length of the wire (l) = 17.0 m
Magnetic field (B) = 0.25 T
Resistance of u-shaped conductor (R) = 25.00 Ω
To find the rate of change of magnetic flux, we can substitute the values into the following equation:
dΦ/dt = -(emf / N)
dΦ/dt = -(V / N)
dΦ/dt = -(IR / N)
We need to find the number of turns of wire (N). This can be calculated using the length of the wire and the speed at which it moves:
N = l / v
N = 17.0 m / 4.6 m/s
N ≈ 3.70 turns
Now we can substitute the values into the equation:
dΦ/dt = -(IR / N)
dΦ/dt = -((0.25 T)(25.00 Ω) / 3.70)
dΦ/dt ≈ -1.351 TΩ/s
Since the magnetic field and the area of the loop do not change, the magnetic flux is a constant value. Therefore, the rate of change of magnetic flux is zero:
dΦ/dt = 0
Solving for -IR/N:
0 = -IR / N
IR / N = 0
Substituting the values:
I(25.00 Ω) / 3.70 = 0
I ≈ 0 A
Therefore, the current flowing in the u-shaped conductor is approximately 0 Amps.