Electromagnetism EMF induction calculations

[imranh88]

Homework Statement

Electromagnetism EMF induction help

Relevant Equations

Faradays law

A square conducting loop of side length a is in a non-uniform magnetic field. The loop occupies the first quadrant of the xy plane, i.e. the space between the origin (x, y) = (0,0) and the point (x,y) = (a, a). The magnetic field is in the +z direction. Develop an expression for the magnitude of the emf induced in the coil, if: a) The magnetic field magnitude is increasing with time and is given by B(x, y, t) = Boxyt3? 18 marks b) The magnetic field magnitude is constant with respect to time and is given by B(x, y) = Box" y, but the loop is moving along the + y direction at a constant speed v? (You can assume that loop position described above is for t=0 s). 18 marks What is the direction of the induced emf for the two cases? 14 marks [20 marks total]

 

[imranh88]

What I did for part a, was integrate the expression for B with respect to x and again with respect to y. then differentiated with respect to t giving: emf= -B0(a^5t^2)/3 is this correct?

 

[berkeman]

Welcome to the PF.

Homework Statement: Electromagnetism EMF induction help
Homework Equations: Faradays law

The magnetic field magnitude is increasing with time and is given by B(x, y, t) = Boxyt3?

Sorry, that is very hard to try to parse. Can you scan the problem and Attach the PDF as a file? It's hard to try to convert what you have posted into a coherent problem statement. Thanks.

What I did for part a, was integrate the expression for B with respect to x and again with respect to y. then differentiated with respect to t giving: emf= -B0(a^5t^2)/3 is this correct?

Also, it would really help if you could post your math equations in LaTeX. There is a tutorial that you can get to via INFO, Help at the top of the page.

 

[DaveE]

Homework Statement: Electromagnetism EMF induction help
Homework Equations: Faradays law

B(x, y, t) = Boxyt3

I have no idea what you are saying here.
Questions that are well constructed and communicated tend to get better answers.

 

[imranh88]

I have no idea what you are saying here.
Questions that are well constructed and communicated tend to get better answers.

for part (a) the equation is: B_{0}x^{2}yt^{3}
for part (b) the equation is: B_{0}x^x{2}y

Thank you guys for helping me, when you really do not have to :)
I have attached the question below.

 

[imranh88]

What I did for part a, was integrate the expression for B with respect to x and again with respect to y. then differentiated with respect to t giving: emf= -B0(a^5t^2)/3 is this correct?

This is my working: with part b having 2 methods as I am not sure on the context of the question. whether the moving loop is moving into the field or if it is moving while already being entirely subject to the field. My guess is the latter, which would correspond to the left hand side marking. the part c is provided at the end of each part, and was done via simple use of Lenz' law.

Please could you help me out and let me know if I am correct.

Thank you all :)

 

[putsub12jk]

for part (b) of this questions the proper to answer questions based on the theme of motional EMF is through integration and the use of the cross product between the vectors v x B. Therefore, your answer using the first method is correct.

 

[imranh88]

for part (b) of this questions the proper to answer questions based on the theme of motional EMF is through integration and the use of the cross product between the vectors v x B. Therefore, your answer using the first method is correct.

Thank you so much!

Can I leave the velocity vector as I did? Also are my directions of induced emf correct? any idea if my part a is correct?

 

[putsub12jk]

you can either express the velocity vector is terms the displacement of the square conducting loop and time, alternatively it would also be good to state the direction of the velocity vector itself i.e. in the +y direction maybe in the step before in your workings. So you can state v sub y hat cross B sub x hat. And yes your direction is also correct as it follows Lenz's Law.

 

[imranh88]

you can either express the velocity vector is terms the displacement of the square conducting loop and time, alternatively it would also be good to state the direction of the velocity vector itself i.e. in the +y direction maybe in the step before in your workings. So you can state v sub y hat cross B sub x hat. And yes your direction is also correct as it follows Lenz's Law.

You have been an invaluable help. Thank you so much. Highly appreciated.