A single loop of wire with an area of 0.0900 m2 is in a uniform magnetic field that has an initial value of 3.80 T, is perpendicular to the plane of the loop, and is decreasing at a constant rate of 0.190 T s. (a) What emf is induced in this loop?

Suppose that f : rn → rm and that a ∈ k, where k is a connected subset of rn . suppose further that for each x ∈ k there exists a δx > 0 such that f(x) = f(y) for all y ∈ bδx (x). prove that f is constant on k; that is, f(x) = f(a) for all x ∈ k

Certain bacteria (such as aquaspirillum magnetotacticum) tend to swim toward the earth’s geographic north pole because they contain tiny particles, called magnetosomes, that are sensitive to a magnetic field. if a transmission line carrying 100 a is laid underwater, at what range of distances would the magnetic field from this line be great enough to interfere with the migration of these bacteria? (assume that a field less than 5% of the earth’s field would have little effect on the bacteria. take the earth’s field to be 5.0 * 10-5 t, and ignore the effects of the seawater.)

You are driving to the grocery store at 20 m/s. you are 110m from an intersection when the traffic light turns red. assume that your reaction time is 0.50s and that your car brakes with constant acceleration. how far are you from the intersection when you begin to apply the brakes? what acceleration will bring you to rest right at the intersection? how long does it take you to stop after the light changes? the known values: vi=20m/s xi=110m t=.50s vf=0m/s xf=0m a=?