Speed and Direction of Electron orbiting within a Solenoid

[rodanme]

In Fig. 28.8, a view of the solenoid, showing the clockwise sense of the current in the windings, is given. An electron is in circular motion near the center of the solenoid, with an orbital diameter of 3.0 cm. The speed of the electron and the sense of the orbital motion are closest to

The diameter of the solenoid is 4 cm
The diameter of the e- orbiting within the solenoid is 3 cm

Homework Equations

r = mv/qb

T= (2*pi*m)/qb

The Attempt at a Solution

Not really sure how to start the problem.
Would I take a conservation of energy approach?
Do I need to try and figure out the B field of the solenoid?

 

[omoplata]

Start with finding the B field of the solenoid.

For the next step, consider that the electron is a charged particle that travels in that B field.

 

[rodanme]

The Equation for B_solenoid = Mu_0 * I * n

how can I find the current of the solenoid?

 

[omoplata]

They have to give the current, or they want the answer in terms of the current.

Judging by the problem statement, this looks like an MCQ problem. If so, do you have the answer list?

If not, do you have this figure 28.8?

 

[asteriatic]

I would first start by examining the given information and identifying any relevant equations or principles that can be applied to the problem. In this case, we are dealing with the motion of an electron within a solenoid, so we can use the equations for circular motion and the Lorentz force.

The first step would be to calculate the magnetic field (B) of the solenoid using the given information. We can use the equation B = μ0 * n * I, where μ0 is the permeability of free space, n is the number of turns per unit length of the solenoid, and I is the current flowing through the solenoid. Once we have the value for B, we can use the equation r = mv/qB to solve for the speed of the electron (v).

Next, we can use the equation T = (2πm)/qB to calculate the period (T) of the electron's orbit. The sense of the orbital motion can be determined by the direction of the current in the solenoid, which is given as clockwise in the problem.

It is also important to note the diameter of the solenoid (4 cm) and the diameter of the electron's orbit (3 cm). This information can be used to calculate the radius (r) of the electron's orbit, which is necessary for the equations used above.

In conclusion, the speed of the electron can be calculated using the equation r = mv/qB, where r is the radius of the orbit, m is the mass of the electron, q is its charge, and B is the magnetic field of the solenoid. The sense of the orbital motion can be determined by the direction of the current in the solenoid, and the period of the orbit can be calculated using the equation T = (2πm)/qB.