29.3 : Biot-Savart Law: Problem-Solving

The magnitude and direction of a magnetic field created by a steady current can be calculated using the Biot-Savart law.

Consider a mobile phone battery bank as a source of steady current, which flows through the wire connected between the two. What is the magnitude of the magnetic field created by this current at a field point P?

To estimate the magnitude of the total magnetic field, we first consider a small current element of length dl, at a distance r from the field point. Now the following parameters are the known quantities:

1. The value of the current
2. The length of the current element
3. The distance between the current element and the field point
4. The angle between the current element and the line joining the field point and the element

The magnitude of the magnetic field due to the current element can be calculated using the equation of Biot-Savart's Law,

The total magnetic field due to the entire wire can be calculated by integrating Equation 1 over the length of the wire.

The right-hand rule gives the direction of the magnetic field. If the thumb points toward the direction of the current, then the fingers curl along the direction of the magnetic field.