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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.

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, = 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.

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

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

Where,

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.

Then $q\left(\stackrel{\to }{v}×\stackrel{\to }{B}\right)=\frac{m{v}^{2}}{r}$

v and B are at right angles

$\therefore qvB=\frac{m{v}^{2}}{r}\phantom{\rule{0ex}{0ex}}⇒r=\frac{mv}{Bq}$

• Time period of the circular motion of a charged particle is given by

⇒

• Angular frequency,

This is often called cyclotron frequency.

Velocity Selector

• Force in the presence of magnâ€¦

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