7) A proton (charge +e) moves from point A to point B under the sole influence of an electric field, losing speed as it does so from m/s to m/s. What is the potential difference between the two points?

) (a) In a thick, straight wire carrying a current that is uniform through its cross section, where is the magnetic field greatest? (b) If the radius of the wire is R and the current is I, what is the value of the maximum magnetic field? ANSWERS WITHOUT EXPLANATIONS WILL NOT BE GIVEN FULL CREDIT.

Let R be the radius of the wire and r be the radius of a loop such that r<R. The loop is centered on the axis of the wire. Let be the current passing through the loop of radius r.

If r>R, then

We see that B is at a maximum when r=R, i.e. .

) A magnetic field that changes with time but is uniform in space is directed along the x-axis. A conducting ring of diameter 7 cm and resistance is placed in the y-z plane. If the current in the ring is 2A, how fast is the magnetic field changing?

I=2A

) A 747 is flying due North at 900 km/h in a location where the Earth's magnetic field consists of an upward vertical component of T and a southward component of T. If the wingtip-to-wingtip length of a 747 is 35 m, find the emf induced across the wings. If the airplane were flying due East instead of due North, how would your answer change?

Ignoring the southward component of the magnetic field, we have

l=35m

Why can we ingore the southward component of the magnetic field? Because it is parallel to the velocity of the airplane wings, so it has no effect on the charges in the wing.

We get the same answer if the plane is flying East. Again, we ignore the southward component because such a component would produce a force on the charges that is pointing either down to the earth or up from the earth. The charges therefore do not move to the ends of the wings under the influence of the southward component of the magnetic field.