Given below is a last minute revisioner of Magnetism for the IIT JEE Main/ Advanced Physics paper . Note that the points covered are based on the exam point of view , and is not meant to be a comprehensive review of the entire magnetism portion.

- A moving charge / flowing electric current produces a magnetic feild ( which is a vector feild ) in addition to the electric force / feild . If a charged particle moves
*parallel to the magnetic feild*, the magnetic force on the charge is zero . The magnetic force differs from an electric force in the fact that a)*it depends on the particle velocity*b)*it’s direction is perpendicular to both*|*v*|*and*|B| and c)*it does no work in displacing a charged particle , provided the magnetic feild is constant*. - Consider a charged particle of mass m moving in an uniform magnetic feild | B | having an initial velocity vector |
*v*| perpendicular to the feild. Then , the path radius = r = m*v*/ qB , angular speed**ω = qB/m**and time period,**T = 2 π m/qB**.If the motion in the uniform magnetic feild is at some arbitrary angle θ with respect to B , then the*path becomes helical*– here there are two velocity components, the perpendicular component moving the charge in a circular path of radius given by**r = m**and the parallel component moving along the feild lines. Pitch*v*1/qB**p = 2 π m vΦ/qB**. - Consider a charged particle moving in an electric feild which is perpendicular to the magnetic feild . Here , the particle velocity is perpendicular to both the feilds. The magnetic feild will rotate the particle in a circle in the x-z plane ,
**||**to the magnetic feild resulting in a helical path with increasing pitch .and*v*x =*v*o cos ( Bqt/m )*v*z =*v*o sin ( Bqt/m ) . - A current carrying conductor of any arbitrary shape in an uniform magnetic feild will experience a force |F| = I|L|x|B| where |L| is the length vector joining initial and final points of a conductor. If it’s a closed loop then |F| = zero. If the magnetic feild is not uniform ,
*various elements of the loop will experience different forces*– means that if the loop is free enough , the*loop could have a circular motion*, ie , |Fr| = zero, but |ζ | may or may not be zero. - Considering the force between two infinite , parallel current carrying conductors , the force / unit length =
**μo I I’/2 π r .**Note that the if the direction of current flow is the same ,*the wires will attract each other*. - As the magnetic feild pattern produced by a small current loop is like a bar magnet, it acts like a magnetic dipole . Here , if the loop is not lying in a single plane ,
*two equal and opposite currents are to be assumed in a single branch*[ note that the net change is zero ] and likewise the required loops are to be considered in different planes . For eg , for a cube of side I carrying a current i ,**|M| net = – i I² ( iˆ + kˆ )**. - If a magnetic dipole changes it’s orientation in a magnetic feild by an infinitesimal angular displacement d Φ ,
*the feild does work dW given by*. The energy present in the loop is**ζ d Φ = dU**, the change in potential energy**U = – |M| |B| .** - A moving point charge with velocity v creates circular magnetic feilds centered on the line of v and which are perpendicular to it. The magnetic feild ,
**|B| = ( μo /4π ) q|v|rˆ/r² .** - For a
*current carrying straight wire*, the feild is zero for points along the length of the wire ,*but not on it*. Here , as the feild is perpendicular to the plane containing both the wire and the point , the*lines of force are concentric circles*which encircle the wire. For the infinite long wire , if the*point is near the end*,**B = ( μo /4π ) 2I/d**and if the*point is near one end*, then,**B = ( μo /4π ) I/d .** - The magnetic feild at the
*centre of a current carrying arc*is**B = μo I/2 R**b) a*point inside a long solenoid***B = μo n I**c) for a*point at one end of a long solenoid***B = μo n I /2**and d) for a*point at a distance R from the centre of a flat strip of width a along it’s perpendicular bisector*,**B = ( μo i /π a ) tan -¹ ( a/2R**) Note – in cases where the*points considered are far from the strip*,**B = ( μo /2π ) ( i/R ) .**