29.3:
Biot-Savart Law: Problem-Solving
A portable power bank behaves like a battery that provides a steady current. The flow of this steady current creates a magnetic field in its vicinity.
Suppose the current flowing through the wire from a power bank to a mobile phone is 1 ampere, what should be the magnetic field at a field point P, twenty centimeters away from a small current element of one millimeter length?
The line joining point P subtends an angle of 45 degrees with the current element.
The magnetic field at the field point due to the current element can be calculated using the Biot-Savart law.
Substituting the known quantities and the value of the constant, the magnetic field due to the current element is estimated to be 1.8 nanotesla.
The right-hand rule gives the magnetic field direction. So, at P, the field direction is considered to be out of the xy plane.
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:
- The value of the current
- The length of the current element
- The distance between the current element and the field point
- 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.
Suggested Reading
- OpenStax. (2019). University Physics Vol. 2. [Web version]. Retrieved from 536-537 https://openstax.org/books/university-physics-volume-2/pages/12-1-the-biot-savart-law