Question

You hold your magnet perpendicular to a bar of copper that is connected to a battery (Figure 20.84). Describe the directions of the components of the electric field at the center of the copper bar, both parallel to the bar and perpendicular to the bar. Explain carefully.

Short answer

The electric field parallel to the bar is directed in the negative$y$ direction.

The electric field perpendicular to the bar is directed in the positive $z$ direction.

Step-by-step solution

Given data

A magnet is held perpendicular to a bar of copper that is connected to a battery.

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 electric fields inside the bar

The copper bar contains moving electrons which experience a magnetic force in the presence of the magnetic field of the magnet. The conventional current is flowing in the negative$y$ direction, from positive to negative of the battery, and thus the electrons are flowing in the positive $y$ direction. The magnetic field from the magnet is directed in the positive$x$ direction. The force on them is thus directed in the positive $z$ direction. The negative charges accumulate into the upper end of the wire. This creates a perpendicular electric field$E_{\perp }$directed in the positive $z$ direction that prevents further flow of electrons towards the far side due to the magnetic force. This is known the Hall field and is perpendicular to the bar. Along with this there is a parallel electric field in the bar due to the battery that is directed in the negative $y$ direction.