Question

A copper wire with square cross section carries a conventional current $\mathit{I}$ to the left (as in Figure 20.83). There is a magnetic field $\mathit{B}$ perpendicular to the wire. Describe the direction of ${\mathit{E}}_{\mathbf{\perp }}$, the transverse electric field inside the wire due to the Hall effect, and explain briefly.

Short answer

The Hall electric field$E_{\perp }$ is directed into the paper which opposes the magnetic force on the flowing electrons in the wire.

Step-by-step solution

Given data

Conventional current in the wire is$I$ .

Magnetic field in the region is$B$ .

Magnetic force

Magnetic force on a moving charge is the product of the magnitude of the charge and the cross product of the velocity vector and the magnetic field.

Determination of the direction of the Hall electric field

The copper wire contains moving electrons which experience a magnetic force in the presence of a magnetic field. The conventional current is flowing to the left and thus the electrons are flowing to the right. The force on them is directed into the paper. The negative charges accumulate into the far end of the wire. This creates a perpendicular electric field $E_{\perp }$ directed into the paper that prevents further flow of electrons towards the far side due to the magnetic force. This is known as the Hall field.