Moving Charges and Magnetism
Concept of magnetic field −
Biot - Savart law and its application to current carrying circular loop
Ampere’s law and its applications to infinitely long straight wire
Straight and toroidal solenoids
Force on a moving charge in uniform magnetic and electric fields
Cyclotron
Force on a current-carrying conductor in a uniform magnetic field
Force between two parallel current-carrying conductors-definition of ampere
Torque experienced by a current loop in uniform magnetic field; moving coil galvanometer-its current sensitivity and conversion to ammeter and voltmeter.
SUMMARY
1. The total force on a charge q moving with velocity v in the presence of magnetic and electric fields B and E, respectively is called the Lorentz force. It is given by the expression: F = q (v × B + E) The magnetic force q (v × B) is normal to v and work done by it is zero.
2. A straight conductor of length l and carrying a steady current I experiences a force F in a uniform external magnetic field B, F = I l × B where|l| = l and the direction of l is given by the direction of the current.
3. In a uniform magnetic field B, a charge q executes a circular orbit in a plane normal to B. Its frequency of uniform circular motion is called the cyclotron frequency. This frequency is independent of the particle’s speed and radius. This fact is exploited in a machine, the cyclotron, which is used to accelerate charged particles.
4. The Biot-Savart law asserts that the magnetic field dB due to an element dl carrying a steady current I at a point P at a distance r from the current element
5.The magnitude of the field B inside a long solenoid carrying a current I is B = µ0 nI.
6. Parallel currents attract and anti-parallel currents repel.
7. A planar loop carrying a current I, having N closely wound turns, and an area A possesses a magnetic moment m where, m = N I A and the direction of m is given by the right-hand thumb rule : curl the palm of your right hand along the loop with the fingers pointing in the direction of the current. The thumb sticking out gives the direction of m (and A) When this loop is placed in a uniform magnetic field B, the force F on it is: F = 0 And the torque on it is, τ = m × B In a moving coil galvanometer, this torque is balanced by a countertorque due to a spring, yielding kφ = NI AB. where φ is the equilibrium deflection and k the torsion constant of the spring.
8. A moving coil galvanometer can be converted into a ammeter by introducing a shunt resistance r s , of small value in parallel. It can be converted into a voltmeter by introducing a resistance of a large value in series.
