Force on a Current - Carrying Conductor in a Uniform Magnetic Field

Consider a straight piece of length x of a wire carrying a current i. Let P be a point on the perpendicular bisector of the piece, situated at a distance d from its middle point. Show that for d >> x, the magnetic field at P varies as 1/d² whereas for d << x, it varies as 1/d.  

When a magnetic compass needle is carried nearby to a straight wire carrying current, then

1. the straight wire cause a noticeable deflection in the compass needle.
2. the alignment of the needle is tangential to an imaginary circle with straight wire as its centre and has a plane perpendicular to the wire.

A wire of length l carries a current i long the x-axis. A magnetic field exists, which is given as `vecB = B_0 (veci + vecj + veck)`  T. Find the magnitude of the magnetic force acting on the wire.

A vertical wire carries a current in upward direction. An electron beam sent horizontally towards the wire will be deflected

Two parallel wires carry currents of 20 A and 40 A in opposite directions. Another wire carying a current anti parallel to 20 A is placed midway between the two wires. T he magnetic force on it will be

Can a charged particle be accelerated by a magnetic field? Can its speed be increased?

A current of 3 A is flowing in a linear conductor having a length of 40 cm. The conductor is placed in a magnetic field of strength of 500 gauss and makes an angle of 30° with the direction of the field. It experiences a force of magnitude: