Need someone to check my equations and work on this induced EMF problem

[dj6859]

Homework Statement

a magnetic field has a magnitude at time t of 4.5x10^-5 T +(2.6x10^-6 T/sec)t. the field points in the positive z-direction.
a rectangular wire loop, which is 0.3 meters by 0.4 meters, lies in the xy-plane.
Note: If the z axis points out of the paper.

a.) What is the induced emf in the loop?

b.) If the wire loop has a resistance of 10 ohms, what is the current in the loop? In a clear diagram, indicate the direction in which that current travels.

c.) How could you re-orient the loop so that the induced emf was only 40% of the value of the value had to find in part (a)?

Relevant Equations

a.) Vinduced= dB/dt*A
b.) I=Vinduced/R
c.) 0.4Vinduced=Vinducedcos(theta)

a magnetic field has a magnitude at time t of 4.5x10^-5 T +(2.6x10^-6 T/sec)t. the field points in the positive z-direction.
a rectangular wire loop, which is 0.3 meters by 0.4 meters, lies in the xy-plane.
Note: If the z axis points out of the paper.

a.) What is the induced emf in the loop?
(2.6x10^-6)(0.12m^2)=0.312x10^-7V

b.) If the wire loop has a resistance of 10 ohms, what is the current in the loop? In a clear diagram, indicate the direction in which that current travels.
I=(0.312x10^-7V)/(10ohm)= 3.18x10^-7V

c.) How could you re-orient the loop so that the induced emf was only 40% of the value of the value had to find in part (a)?
0.4=cos(theta)
theta=66.42degrees
90-23.58degrees

 

[Charles Link]

Maybe my arithmetic is wrong, but I think you have a couple of careless errors in the exponents and scientific notation of parts (a) and (b). Please double-check your answers there. $\\$ Also you need to determine the direction of the current for part (b). To describe it without a diagram, looking at the loop with positive z-pointing at you, is the current clockwise or counterclockwise? For a hint at this part, the magnetic field created from any current flow must oppose the change in the magnetic field that is occurring. $\\$ For part (c), you got it pretty much correct, but the normal to the plane of the loop needs to be at angle 66.4 degrees w.r.t. the z-axis. That is how such an orientation is normally described.