moving charges and magnetism

What is the Biot-Savart law for the magnetic field due to a small current element?

θ = angle between dl (current direction) and r (line joining the current to the observation point).

What is the magnetic field at the centre of a circular current-carrying loop of radius a?

What is the magnetic field on the axis of a circular coil at distance x from its centre?

What is the magnetic force on a charged particle moving in a magnetic field?

θ = angle between velocity v and magnetic field B. this is lorenz force

what is the work done in magnetic field on a charged particle in a moving field

The work done by a magnetic field on a charged particle is zero. This is because the magnetic force is always at a right angle (perpendicular) to the velocity and motion of the particle, meaning it changes the direction of the charge but never changes its speed or kinetic energy.

What happens to a charged particle's path when it enters a magnetic field perpendicular to its velocity?

Magnetic force pro

provides the centripetal force, so the particle moves in a circular path.

What is the time period of a charged particle moving in a circular path in a uniform magnetic field?

What is the magnetic force on a current-carrying conductor of length l in a magnetic field?

θ = angle between the direction of current I and the magnetic field B

What is the value of μ_o/4π?

What is the velocity of a charged particle passing undeflected through crossed electric and magnetic fields?

What is Ampere's circuital law?

where I is the current enclosed by the Amperian loop.

Magnetic field due to a long straight current-carrying wire?

where r is the perpendicular distance from the wire.

What is the magnetic field at distance r inside a long cylindrical conductor of radius a, carrying uniformly distributed current I, when r<a?

where a is the actual radius and r is the radius for amperian loop

What is the magnetic field at the surface of long cylindrical conductor of radius a, conductor (r=a)?

What is the magnetic field outside the same conductor (r>a)?

What is the force per unit length between two long parallel current-carrying wires?

where d is the separation between the wires.

Magnetic field inside a long current-carrying solenoid?

this is at the centre where both sides of the solenoid contribute to B

define 1 ampere

1A is the current which flows when two long parallel wires are separated by a distance of 1m, produce a force per unit length of 2x10^-7 N/m in both the wires, when placed in a vacuum.

What is the torque on a rectangular current-carrying coil in a magnetic field?

θ is the angle between the area vector A (normal to the coil) and B.

What is the magnetic dipole moment of a current-carrying coil?

What is the current sensitivity of a moving-coil galvanometer?

What is the voltage sensitivity of a moving-coil galvanometer?

What is the formula for converting a galvanometer into an ammeter?

• S = shunt resistance

• G = galvanometer resistance

• Ig​ = full-scale galvanometer current

• I = desired maximum current of the ammeter

What is the formula for converting a galvanometer into a voltmeter?

magnetic field at the centre of a toroid formula