Question

Write an equation for the magnetic field vector b generated by the current at an arbitrary point in terms of i, the length element dl, and the vector for the distance r from dl to the point.

Answer 1

The magnetic field vector B generated by the current at an arbitrary point in terms of i, the length element dl, and the vector for the distance r from dl to the point is given by the equation dB =  μ0/4 π ∫ (dl x r)/r$r^{3}$

Biot – Savart Law and its Applications:

The Biot – Savart Law gets its name from Jean-Baptiste Biot and Felix Savart. This is a formula that describes the relationship between force, displacement, and velocity. It plays a huge role in the branch of electromagnetism. This law is used to derive the equation between the magnetic field which is produced due to the flow of a constant electric current.

The equation of Biot – Savart law is

dB = μ0/4 π ∫ {(idl sinΦ)/r2}

Here,

I is the current,

dl is the small length of the wire. As the direction of this length is along the current hence it forms the vector idl.

r is the position vector of the point in question which is drawn from the current element and

Φ is the angle between the two.

Applications of Biot – Savart Law

• It helps in the calculation of magnetic field in an infinitely long straight wire with constant current,

• Calculation of magnetic field in the center of current carrying arc can be done by this,

• To calculate the magnetic field along the axis of a circular current carrying coil, this law can be used.

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