Magnetic Fields due to Electric Current

Magnetic field due to current element, Biot-Savart; Magnetic field on the axis of a circular current loop

• Static charges produce an electric field while current or moving charges produce magnetic field (B).

• Magnetic field of several sources is the vector addition of magnetic field of each individual source.

Lorentz Force

• Consider a point charge q moving in the presence of both electric and magnetic fields.

Let

q − Point charge

v − Velocity of point charge

t − Time

r − Distance

B (r) − Magnetic field

E (r) − Electric field

∴ Force on the charge, = F_electric + F_magnetic

This force is called Lorentz force.

• Force due to magnetic field depends on q, v, B. Force on negative charge is opposite to that of positive charge.

• Magnetic force is a vector product of velocity (v) and magnetic field (B). It vanishes, if v and B are parallel or anti-parallel.

• Magnetic force is zero, if charge is not moving.

• Unit of magnetic field (B) is tesla (T).

Magnetic Force on a Current Carrying Conductor Placed in Magnetic Field:

A straight rod carrying current is considered.

Let

A − Cross-sectional area of the rod

l − Length of the rod

n − Number density of mobile charge carriers

I − Current in the rod

v_d − Average drift velocity of mobile charge carrier

B − External magnetic field

Force on the carriers,

F = (nAl) qv_d × B

Since current density, j = nqv_d

∴ F = [(nqv_d)Al] × B

F = [jAl] × B

F = I l × B

Where,

l is the vector magnitude of length of the rod

• For a wire of arbitrary shape,

• Static charges produce an electric field while current or moving charges produce magnetic field (B).

• Magnetic field of several sources is the vector addition of magnetic field of each individual source.

Lorentz Force

• Consider a point charge q moving in the presence of both electric and magnetic fields.

Let

q − Point charge

v − Velocity of point charge

t − Time

r − Distance

B (r) − Magnetic field

E (r) − Electric field

∴ Force on the charge, = F_electric + F_magnetic

This force is called Lorentz force.

• Force due to magnetic field depends on q, v, B. Force on negative charge is opposite to that of positive charge.

• Magnetic force is a vector product of velocity (v) and magnetic field (B). It vanishes, if v and B are parallel or anti-parallel.

• Magnetic force is zero, if charge is not moving.

• Unit of magnetic field (B) is tesla (T).

Magnetic Force on a Current Carrying Conductor Placed in Magnetic Field:

A straight rod carrying current is considered.

Let

A − Cross-sectional area of the rod

l − Length of the rod

n − Number density of mobile charge carriers

I − Current in the rod

v_d − Average drift velocity of mobi…