Please solve the following problems. You must show all work.

1) If a charge particle move in a straight line and there no other forces on it except possibly from a magnetic field, can you say with certainty that no magnetic field is present? Explain.

2) In a velocity selector, the uniform magnetic field of 1.5 T is produced by a large magnet. Two parallel plates with a separation of 1.5 cm produce the perpendicular electric field. What voltage should be applied across the plates so that:

a) A singly ionized ion traveling 8.0 x 10^{4} m/s will pass through undeflected.

b) A double ionized ion traveling at the same speed will pass through undeflected.

3) A horizontal magnetic field of 1.0 x 10^{-4} T is at an angle of 30^{o} to the direction of the current in a straight wire 75 cm long. If the wire carries a current of 15 A, what is the magnitude of the force on the wire?

4) An electron travels at a speed of 2.0 x 10^{4} m/s through a uniform magnetic field of strength 1.2 x 10^{-3} T. What is the magnitude of the magnetic force on the electron if its velocity and the magnetic field:

a) Are perpendicular

b) Make an angle of 45^{o}

c) Are parallel

d) Are exactly opposite?

5) A square loop of wire with sides of length 40 cm is in a uniform magnetic field perpendicular to its area If the field’s strength is 100 mT an it decays to zero in 0.010 seconds:

a) What is the magnitude and of the average emf induced in the loop?

b) What happens to the emf is the side lengths are reduced by a factor of ½?

6) The armature of an ac generator has 100 turns. Each turn is a rectangular loop measuring 8.0 cm by 12 cm. The generator has a sinusoidal voltage output with an amplitude of 24 V. If the magnetic field of the generator is 250 mT,

a) With what frequency does the armature turn?

b) If you double the B and cut in half, how does this affect the amplitude?

7) An ac generator supplies 20 A at 440 V to a 10,000 V power line. If the step up transformer has 150 turns in its primary coil, how many turns are in the secondary coil?

Hint to problem 1, think about the angle between B field and velocity of ion.