Question

A strip of copper carries current in the \(+x\) -direction. There is an external magnctic field directed out of the page. What is the direction of the Hall electric field?

Short answer

Answer: The direction of the Hall electric field is in the \(-y\) direction.

Step-by-step solution

Understanding the problem and setting up the coordinates

The magnetic field is given in the \(z\) direction, pointing out of the page. The current is in the \(x\) -direction, flowing through the copper strip. Our goal is to find the direction of the Hall electric field, which is perpendicular to both the current and the magnetic field.

Right-hand rule for the magnetic force on moving charges

We'll use the right-hand rule to determine the direction of the force experienced by the mobile charges as they move through the strip due to the external magnetic field. Place the thumb of your right hand in the direction of the current (in this case, the \(+x\) direction), and let your fingers curl in the direction of the magnetic field (coming out of the page, or in the \(+z\) direction). The direction in which your palm faces represents the direction of the force experienced by the positively charged particles (\(+q\)) in the copper strip. In this case, your palm will be facing in the \(+y\) direction.

Determine the direction of the Hall electric field

Now that we know the direction of the force experienced by the positive charges in the copper strip, we can conclude that the Hall electric field will be established in the opposite direction to this force. Therefore, the Hall electric field is in the \(-y\) direction. So the direction of the Hall electric field is in the \(-y\) direction.