Question

A proton, moving in negative \(y\) -direction in a magnetic field, experiences a force of magnitude \(F\), acting in the negative \(x\) -direction. a) What is the direction of the magnetic field producing this force? b) Does your answer change if the word "proton" in the statement is replaced by "electron"?

Short answer

Answer: The direction of the magnetic field producing this force on both the proton and electron is in the positive z-direction.

Step-by-step solution

Apply the Right-Hand Rule for the Proton

To determine the direction of the magnetic field (B), we can use the right-hand rule related to the magnetic force experienced by a moving charged particle. The formula for the magnetic force experienced by a charged particle moving with velocity (v) in a magnetic field (B) is given by: F = q(v x B), where q is the charge of the particle and x denotes the cross product. Since the proton has a positive charge, we can use the right-hand rule as follows: 1. Point your thumb in the direction of the proton's velocity (negative y-direction). 2. Point your other fingers in the direction of the force (negative x-direction). 3. Your palm should face the direction of the required magnetic field. As you perform these steps, you should notice that the direction of the magnetic field is in the positive z-direction.

Determining the Direction of the Magnetic Field

By applying the right-hand rule as described in step 1, we can conclude that the direction of the magnetic field producing this force on the proton is in the positive z-direction. b) For this part, we need to find out if the direction of the magnetic field changes when the word "proton" in the statement is replaced by "electron".

Apply the Right-Hand Rule for the Electron

Since the electron has a negative charge, we need to adjust the application of the right-hand rule accordingly. We can do this by using the left-hand rule for negatively charged particles as follows: 1. Point your thumb in the direction of the electron's velocity (negative y-direction). 2. Point your other fingers in the direction of the force (negative x-direction). 3. Your palm should face the direction of the required magnetic field. As you perform these steps, you should notice that the direction of the magnetic field is in the positive z-direction.

Comparing the Directions of the Magnetic Fields

By applying the left-hand rule for the electron, we can conclude that the direction of the magnetic field producing this force on the electron is also in the positive z-direction. In conclusion, the answer does not change if the word "proton" in the statement is replaced by "electron". The direction of the magnetic field producing this force remains in the positive z-direction.