Question

An experimentalist fires a beam of electrons, creating a visible path in the air that can be measured. The beam is fired along a direction parallel to a current-carrying wire, and the electrons travel in a circular path in response to the wire's magnetic field. Assuming the mass and charge of the electrons is known, what quantities would you need to measure in order to deduce the current in the wire and the magnetic field due to that current?

Answer 1

Answer:  

Velocity of the electron in the beam.

Radius of the circulating electrons due to the magnetic field.

Explanation:

We have a Mathematical expression for the force on a moving charge in a magnetic field as:

$F=q.v.B.sin \theta$ ...........................(1)

where:

q= charge on the particle in coulomb

v= velocity of the charge projected into the magnetic field

B= intensity of the magnetic field in tesla

$\theta$= angle between the velocity and direction of magnetic field

For the forces on rotating mass we have the formula:

$F=m.\frac{v^2}{r}$..........................................(2)

where:

m= mass of the charged particle

v= velocity of projection of charge into the magnetic field

r= radius of the path traced  by the charge in the magnetic field

From eq. (1) and (2) we can calculate the magnetic field .

Now,

Using Ampere's Law we have:

$B = \frac{\mu_0 .I}{2 \pi r}$

where:

I= current in the wire

$\mu_0=$ The permeability of free space.

r= radial distance from the current carrying wire( in this case it is same as the radius of the circular path)