Moving Charges And Magnetism
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.
Consider a point charge q moving in the presence of both electric and magnetic fields.
q − Point charge
v − Velocity of point charge
t − Time
r − Distance
B (r) − Magnetic field
E (r) − Electric field
∴ Force on the charge, = Felectric + Fmagnetic
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.
A − Cross-sectional area of the rod
l − Length of the rod
n − Number density of mobile charge carriers
I − Current in the rod
vd − Average drift velocity of mobile charge carrier
B − External magnetic field
Force on the carriers,
F = (nAl) qvd × B
Since current density, j = nqvd
∴ F = [(nqvd)Al] × B
F = [jAl] × B
F = I l × B
l is the vector magnitude of length of the rod
For a wire of arbitrary shape,
When a charged particle having charge q moves inside a magnetic field with velocity v, it experiences a force .
When is perpendicular to, the force on the charged particle acts as the centripetal force and makes it move along a circular path.
Let m be the mass of charged particle and r be the radius of the circular path.
v and B are at right angles
Time period of the circular motion of a charged particle is given by
This is often called cyclotron frequency.
Force in the presence of magn…
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