Moving Charges And Magnetism
Magnetic field due to current element, Biot-Savart; Magnetic field on the axis of a circular current loop
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Static charges produce an electric field while current or moving charges produce magnetic field (B).
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Magnetic field of several sources is the vector addition of magnetic field of each individual source.
Lorentz Force
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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.
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Force due to magnetic field depends on q, v, B. Force on negative charge is opposite to that of positive charge.
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Magnetic force is a vector product of velocity (v) and magnetic field (B). It vanishes, if v and B are parallel or anti-parallel.
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Magnetic force is zero, if charge is not moving.
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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
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For a wire of arbitrary shape,
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When a charged particle having charge q moves inside a magnetic field with velocity v, it experiences a force .
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When is perpendicular to, the force on the charged particle acts as the centripetal force and makes it move along a circular path.
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Let m be the mass of charged particle and r be the radius of the circular path.
Then
v and B are at right angles
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Time period of the circular motion of a charged particle is given by
⇒
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Angular frequency,
This is often called cyclotron frequency.
Velocity Selector
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Force in the presence of magn…
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