A constant magnetic field passes through a single rectangular loop whose dimensions are 0.35 m x 0.55 m. The magnetic field has a magnitude of 2.1 T and is inclined at an angle of 55° with respect to the normal to the plane of the loop.
(a) If the magnetic field decreases to zero in a time of 0.37 s, what is the magnitude of the average emf induced in the loop?
_________V
Emf = -N cos theta (B-B0/t-t0)
Emf = -1(cos 55degrees)(0-2.1T/0.37s-0)
Emf = -1(0.573576436)(-2.1T/0.37s)
Emf = (-0.573576436)(-5.675675676)
Emf = 3.25543 V
(b) If the magnetic field remains constant at its initial value of 2.1 T, what is the magnitude of the rate (delta A) / (delta t) at which the area should change so that the average emf has the same magnitude as in part (a)?
_________m^2/s
delta A/ delta t= Emf / NB cos theta
= 3.25543 V / (1)(2.1T)(cos 55 degrees)
= 2.7027 m^2/s
I agree with your formula and numbers, but you are carrying too many significant figures, especially with the cosine. There should only be two significant figures.
I have preferred to avoid Electricity and Magnetism questions because I don't remember the subject very well, and my favorite college textbook on that subject was destroyed in a house fire.
Why don't magnets like talking to each other? Because they always have opposite "poles"! Ba dum tss!
(a) The magnitude of the average emf induced in the loop is 3.25543 V.
(b) The magnitude of the rate (delta A) / (delta t) at which the area should change so that the average emf has the same magnitude as in part (a) is 2.7027 m^2/s.
To find the magnitude of the average emf induced in the loop, we can use the formula:
Emf = -N cos θ (B - B0) / (t - t0)
Where:
- N is the number of turns in the loop (assumed to be 1 in this case)
- θ is the angle between the magnetic field and the normal to the plane of the loop (given as 55°)
- B is the final magnetic field (0 T in this case, as it decreases to zero)
- B0 is the initial magnetic field (given as 2.1 T)
- t is the final time (0.37 s in this case)
- t0 is the initial time (0 s, as the field starts at 2.1 T)
Now, let's substitute the given values into the formula:
Emf = -1 × cos(55°) × (0 - 2.1 T) / (0.37 s - 0)
Calculating this expression, we get:
Emf = -1 × 0.573576436 × (-2.1 T) / (0.37 s)
Simplifying further:
Emf = (-0.573576436) × (-5.675675676)
This simplifies to:
Emf = 3.25543 V
So, the magnitude of the average emf induced in the loop is 3.25543 V.
Moving on to part (b), we need to find the rate of change of area (delta A / delta t) that would result in the same average emf magnitude as in part (a).
The formula to calculate the rate of change of area is:
delta A / delta t = Emf / (N × B × cos θ)
Substituting the given values:
delta A / delta t = 3.25543 V / (1 × 2.1 T × cos(55°))
Calculating this expression, we get:
delta A / delta t = 2.7027 m²/s
Therefore, the magnitude of the rate of change of area required for the average emf to have the same magnitude as in part (a) is 2.7027 m²/s.