Question

Use the oscilloscope to measure the voltage across a large solenoid as a pair of rattlesnake eggs are inserted from opposite sides of that solenoid and allowed to collide in the middle. Question 1: How does the speed of the eggs affect the measurement?

Answer 1

For a large solenoid, the B-field within is nearly uniform, while the field outside is close to zero. The field within the coil can be calculated from Ampere’s Law:

where, n is the number of turns in the coil per unit length, I is the current through the coil and is the permeability of the medium inside the coil. The movement of rattlesnake eggs create a change in the value of permeability of the medium inside the coil which causes a change in the magnetic field.

Similarly, Faraday's law relates the emf induced (E) in a wire loop of turns (here solenoid) to the rate of change of the magnetic flux through it, and Lenz's law states that an induced emf drives a current which produces a magnetic field opposing the change in magnetic flux.

In your problem, if the eggs move from opposite direction with same speed, the induced emf will be produced in the opposite direction of same magnitude. Therefore, there will be no change in the voltage across a large solenoid.

But, if they moves in different speed, then the net induced voltage will have some positive value in the direction of the voltage across the solenoid (let say vi). The voltage across the solenoid is V without any egg inside it. Therefore, the voltage across the solenoid with the eggs moving through it will be as measured by the oscilloscope