A rectangular coil 0.065 m by 0.080 m is positioned
so that its cross-sectional area is perpendicular
to the direction of a magnetic field.
The coil has 66 turns and a total resistance of
7.6 Ω and the field decreases at a rate of 2.5
T/s.
What is the magnitude of the induced current
in the coil?
Answer in units of A.
I really need help... Its due today
see what I just posted. current= EMF/resistance.
To find the magnitude of the induced current in the coil, we can use Faraday's law of electromagnetic induction. According to Faraday's law, the magnitude of the induced current is equal to the rate of change of magnetic flux through the coil.
The formula for magnetic flux is given by:
∅ = B x A x cosθ
where:
∅ is the magnetic flux,
B is the magnetic field,
A is the cross-sectional area of the coil,
θ is the angle between the magnetic field and the normal to the coil.
In this case, the cross-sectional area of the coil is given as 0.065 m x 0.080 m = 0.0052 m².
The magnetic field is decreasing at a rate of 2.5 T/s.
Next, we need to find the rate of change of magnetic flux (∆∅/∆t) through the coil. This can be calculated by multiplying the rate of change of the magnetic field (∆B/∆t) by the cross-sectional area (A) of the coil.
∆∅/∆t = (∆B/∆t) x A
Substituting the values:
∆∅/∆t = (-2.5 T/s) x (0.0052 m²)
Now, we have the rate of change of magnetic flux. But since there are 66 turns in the coil, we need to multiply the rate of change of magnetic flux by the number of turns.
∆∅/∆t × N = (-2.5 T/s) x (0.0052 m²) x (66 turns)
Finally, to find the magnitude of the induced current (I), we use Ohm's Law, which states that I = V/R, where V is the induced voltage and R is the resistance of the coil.
Since V = -∆∅/∆t × N (the negative sign is due to Lenz's Law), we can substitute this into Ohm's Law:
I = (-∆∅/∆t × N) / R
Substituting the values:
I = [(-2.5 T/s) x (0.0052 m²) x (66 turns)] / 7.6 Ω
Now, perform the calculations to find the magnitude of the induced current in the coil, and make sure to round the answer to the appropriate number of significant figures.