I got the correct answer for part (a) but I am unsure of how to tackle part (b). Please help!!!
Interactive LearningWare 22.2 at wiley/college/cutnell reviews the fundamental approach in problems such as this. A constant magnetic field passes through a single rectangular loop whose dimensions are 0.35 m 0.55 m. The magnetic field has a magnitude of 2.1 T and is inclined at an angle of 75° with respect to the normal to the plane of the loop.
(a) If the magnetic field decreases to zero in a time of 0.46 s, what is the magnitude of the average emf induced in the loop?
emf = -N (cos 75) (B-B0/t-t0)
emf = -1 (0.258819)(-2.1T/0.46s)
emf = -1 (0.258819)(-4.565217391)
emf = 1.18156V
(b) If the magnetic field remains constant at its initial value of 2.1 T, what is the magnitude of the rate A / t at which the area should change so that the average emf has the same magnitude as in part (a)?
__________ m2/s
Your use of significant digits baffles me. There is only two significant digits given in the problem.
This is a non trivial error in physics, especially in labs involving measurement. One cannot create precision with calculators.
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/farlaw.html#c1 is a good summary of Faradays law. You are dealing with changing generating an emf by a changing magnetic flux, magnetic flux is B*area
So Faradays law will be
emf=-N d flux /dt
emf=-N (A*dB/dt + B*dArea/dt)
in part a, dArea/dt was zero. In the second part, dB/dT is zero. So for the same emf in the second part, dArea/dt=dB/dt ,
B*dArea/dT=-4.6 m^2/second
B=2.1T, and since area is tilted, the effective cross sectional area is
L*W*cosTheta or A cosTheta.
B*cosTheta* dA/dt=emf
I am not so comfortable with the "correct"response in a) Where is area in the calculations? One cannot ignore the area, as you are dealing with flux. Flux is B*area.
YOu may find some benefit in reviewing Faraday's law.
To find the magnitude of the rate A/t at which the area should change, we can start by using the formula for the average emf induced in the loop:
emf = -N(cosθ)(B/t)
In part (a), we found that the magnitude of the average emf induced in the loop is 1.18156 V. So, we can set this value equal to the expression above:
1.18156 V = -N(cosθ)(B/t)
Since we want to find the magnitude of the rate A/t at which the area should change, we need to express the emf in terms of A and t. Let's rewrite the expression for emf in terms of A and t:
emf = -N(A/t)(B/A)
The area A of the rectangular loop is given by A = length * width = 0.35 m * 0.55 m = 0.1925 m^2.
Now, let's substitute the values into the equation for emf:
1.18156 V = -N(B/t)(B/0.1925 m^2)
Since B = 2.1 T, we can plug in this value:
1.18156 V = -N(2.1 T/t)(2.1 T/0.1925 m^2)
Next, let's consider the magnitude of the average emf (-1.18156 V) and solve for the magnitude of A/t:
1.18156 V = (2.1 T^2/t)(-1.18156 V/0.1925 m^2)
Simplifying the equation, we can cancel out the voltage units:
1 = 2.1 T^2/t * -1/0.1925 m^2
Now, we can solve for the magnitude of A/t:
A/t = 1 * 0.1925 m^2 / 2.1 T^2
A/t = 0.0917 m^2/T^2
Therefore, the magnitude of the rate A/t at which the area should change so that the average emf has the same magnitude as in part (a) is 0.0917 m^2/T^2.