Question

1. A steady, uniform magnetic field of magnitude B, exists in the horizontal, shaded region. This field is directed downward, as indicated. A rectangular loop of rigid, conductive wire, of length L, width W mass m, and resistance R, is initially at rest on a horizontal, frictionless surface, with its east end located at the edge of the field, as shown couninate natn north L easr side 1 X X X X W X X side 2 X X d Then you begin to push the loop so that it has a constant eastward acceleration until its east end is a distance d into the field (where d <L). From that moment (call it = 0), you maintain the loop's motion at a steady velocity v eastward. The list of known values: B. L. W,m, R, v, d, b. Ho Find algebraic expressions for the following, expressing your results using only known values, and for full credit, you must show that the units of your solutions are also correct. From the moment you begin to push until the moment defined as t 0, how much work have you done on the loop? a. b. As you push the loop into the field., what is the direction of the force that side 2 of the loop exerts on side 1? Why doesn't the loop get deflected as a result of this force? Suppose that the field strength varies according to this time function: B() = Be, where b isa known constant (and t0 at the moment defined above). What fraction of the loop's area will still be outside the field when the magnetic field in that external area reverses direction? (You may assume that the reversal occurs while the loop's right end is still in the field and its left end is still outside the field.) c.

Answer 1

A steady, uniform negative field at magnitude B_0 exists in the horizontal. A rectangular loop at rigid, conductive of length = l, width = w, mass = m, Resistance = R, when, d < L t = 0 moment you begin on push until moment distant t = 0, work done = x middot d X = -I WB_0 dx = -sigma /R WB_0 middot d_x [sigma = -d theta/d t] = -d/dt (B_0 w_x) work done = -B_0 W. upsilon work done = -B_0 w upsilon work done = integral^d_0 - sigma/R w B_0. dx work done = B_0^2 w^2 upsilon/R d push the loop into the field, the direction at the force that side z at the loop exist on side 1.force on side 2 is equal and opposite to force in side 1 as f = I l times B \r\n field strength varies ascending to their time function. B(t) = B_0 e_-3bt where, b = constant t = 0 at the moment