Moving Charges and Magnetism Mind Map

Lorentz force is the total force on a charge q moving with velocity v in the presence of electric field E and magnetic field B, given by F = q(E + v x B).

Always mention the angle between v and B, the sign of charge, and the direction rule. In numerical questions, use the magnitude of charge for radius and then discuss direction separately.

Biot-Savart law gives the small magnetic field dB produced at a point by a small current element I dl, with dB = (mu0/4pi) (I dl x r_hat)/r^2.

In derivations, clearly show the vector direction and explain which components cancel by symmetry before writing the final field expression.

The magnetic field at a point on the axis of a circular loop of radius R carrying current I is B = mu0 I R^2/[2(R^2 + x^2)^(3/2)], directed along the axis of the loop.

In derivation questions, state the symmetry cancellation clearly. This is often where marks are awarded before the final formula.

Ampere's circuital law states that the line integral of magnetic field around a closed path equals mu0 times the net current enclosed by that path: integral B dot dl = mu0 I_enc.

Choose the Amperian loop from symmetry. If B is not constant or not parallel to dl, the law is true but may not directly give B in a simple form.

Two long parallel current-carrying wires exert magnetic forces on each other because each wire lies in the magnetic field produced by the other. The force per unit length is F/l = mu0 I1 I2/(2pi d).

After calculating force per unit length, always add the nature of force. Direction carries marks in conceptual and assertion-reason questions.

A current loop placed in a magnetic field experiences a torque tau = N I A B sin theta, where N is number of turns, I is current, A is area, B is magnetic field, and theta is the angle between the magnetic moment and magnetic field.

For galvanometer answers, write both torques: deflecting torque NIAB and restoring torque k phi. Then equate them to show phi is proportional to I.