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 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.
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.
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