Question

The square loop shown in the figure moves into a 0.80T magnetic field at a constant speed of 10m/s. The loop has a resistance of 0.10Ω, and it enters the field at t = 0s.

Answer 1

Find the induced current in the loop as a function of time. Give your answer as a graph of I versus t from t = 0s to t = 0.020s.

Answer 2

There's a dialogue box to draw a line, but I wouldn't know where the points go. Also,

What is the maximum current?


What is the position of the loop when the current is maximum?
The maximum current is when the loop is at the beginning of the region of the field.
The maximum current is when the loop is at the end of the region of the field.
The maximum current is when the loop is halfway into the region of the field.

Answer 3

this is Faraday's law starting with V = - dø/dt

we need to find the flux, and the symmetry is extremely helpful here.

ø = B A -- field is perp to the loop, B is constant, so we have V = - B dA/dt, I = V/R = -B/R dA/dt

the relationship between A and x on the diagram can be shown geometrically or using integration:



because it's a square, the are enclosed between the vertex and a distance x is A = x^2. that's the critical part.....

thus dA/dt = dA/dx * dx/dt


giving I = -B/R dA/x * dx/dt

where dx/dt = 10 m/s, dA/dx = 2x.

once you are half way, when x = 10/root(2), the symmetry remains but the area starts decreasing.

the area then is 100 - y^2, where y is the distance from the other vertex and y + x = 10 root(2)

see drawing, you can get a different equation in x for A(x) and just proceed as above.