H2 Physics 17 - Electromagnetic Forces: Force on a Current-Carrying Conductor

Step 1 - State the problem

A straight wire of length zero point two five metres carries a current of four point zero amperes.

Step 1 - State the problem

It is placed in a uniform magnetic field of flux density zero point three zero tesla.

Step 1 - State the problem

The wire makes an angle of thirty degrees with the field. We want to find the force on the wire.

Step 2 - Recall the force formula

The force on a current-carrying conductor in a magnetic field is F equals B I L sine theta.

Step 2 - Recall the force formula

Here theta is the angle between the current direction and the magnetic field direction.

Step 2 - Recall the force formula

When the wire is perpendicular to the field, sine theta equals one and the force is maximum.

Step 2 - Recall the force formula

When the wire is parallel to the field, sine theta equals zero and there is no force.

Step 3 - Substitute and calculate

Substituting: F equals zero point three zero times four point zero times zero point two five times sine thirty degrees.

Step 3 - Substitute and calculate

Sine of thirty degrees is zero point five.

Step 3 - Substitute and calculate

So F equals zero point three zero times four point zero times zero point two five times zero point five.

Step 4 - Determine the direction using Fleming's left-hand rule

To find the force direction, use Fleming's left-hand rule.

Step 4 - Determine the direction using Fleming's left-hand rule

Point the first finger along the magnetic field direction.

Step 4 - Determine the direction using Fleming's left-hand rule

Point the second finger along the conventional current direction.

Step 4 - Determine the direction using Fleming's left-hand rule

The thumb then points in the direction of the force, or the motion of the conductor.

Step 4 - Determine the direction using Fleming's left-hand rule

Note that the force is always perpendicular to both the current and the field.

Step 5 - Extension: what if the wire were perpendicular to the field?

If the wire were perpendicular to the field, theta would be ninety degrees and sine ninety equals one.

Step 5 - Extension: what if the wire were perpendicular to the field?

The force would then be zero point three zero times four point zero times zero point two five, which gives zero point three zero newtons.

Step 5 - Extension: what if the wire were perpendicular to the field?

This is double the force at thirty degrees.

Step 5 - Extension: what if the wire were perpendicular to the field?

A common exam mistake is using cosine instead of sine. Remember: the force depends on the component of current perpendicular to B, so it is sine theta, not cosine theta.