(a) Describe an activity to show that a current carrying conductor, placed in an external magnetic field experiences a force. (b) Imagine that you are sitting in a chamber with your back to one wall. An electron beam, moving horizontally towards the front wall from the back wall, is deflected by a strong magnetic field to your right side. Find the direction of the magnetic field.

(a) Activity to show the force on a current-carrying conductor in a magnetic field

Take a small aluminium rod AB (about 5 cm long) and suspend it horizontally from a stand using two flexible connecting wires. Place a strong horse-shoe magnet so that the rod lies between its two poles, with the north pole vertically below and the south pole vertically above the rod — so the magnetic field between the poles points vertically upward through the rod. Connect the rod in series with a battery, a plug key and a rheostat.

When the key is closed and current is passed through the rod from end B to end A, the rod is observed to get displaced towards the left. On reversing the direction of current (A to B), the rod is displaced towards the right. Similarly, if the current direction is kept the same but the magnet's poles are interchanged (field reversed to point downward), the direction of displacement again reverses.

This shows that:

• A current-carrying conductor placed in a magnetic field experiences a force.
• The direction of this force reverses when either the current or the field is reversed.
• The displacement (force) is maximum when the current direction is at right angles to the field, and in that case the direction of the force is given by Fleming's left-hand rule: if the forefinger points along the field and the middle finger along the current, the thumb gives the direction of the force (motion) — with the thumb, forefinger and middle finger held mutually perpendicular.

(b) Direction of the magnetic field

Set up directions as seen by the person in the chamber: let $+y$ be the direction from the back wall to the front wall (the direction of electron motion), $+x$ be the person's right, and $+z$ be vertically upward.

• Electron beam velocity: along $+y$ (back wall $\rightarrow$ front wall).
• Since electrons are negatively charged, the conventional current $I$ flows opposite to the electron motion, i.e. along $-y$ (front wall $\rightarrow$ back wall).
• The force (deflection) on the beam is towards the person's right, i.e. along $+x$.

Applying Fleming's left-hand rule with the middle finger along the current ($-y$, i.e. pointing from front wall towards the back wall) and the thumb along the force ($+x$, to the right), the forefinger — which gives the direction of the magnetic field — points along $-z$.

$$-z \; \text{direction} = \text{vertically downward}$$

Hence, the magnetic field must be directed vertically downward (from the ceiling towards the floor of the chamber).