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?

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:

...........................(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

= angle between the velocity and direction of magnetic field

For the forces on rotating mass we have the formula:

..........................................(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:

where:

I= current in the wire

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)

the order for strong to weak forces such as

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force

the fundamental forces are those forces that act between to objects or element to make interactions. there are four types of fundamental forces such as strong and weak nuclear forces (due to protons and electrons), electromagnetic force (due to the motion of electrons) and gravitational force (due to orbital movement of the planet). if these forces are arranged on the basis of their maximum strength then the order is

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force