Q.A conductor of linear mass density 0.2 g m$^{-1}$ is suspended by two flexible wires as shown in the figure (a horizontal straight conductor hung level by a vertical flexible wire at each end). Suppose the tension in the supporting wires is zero when the conductor is kept inside a magnetic field of 1 T whose direction is into the page. Compute the current inside the conductor and also the direction of the current. Assume $g=10$ m s$^{-2}$.

Magnetic Force on Current

Imagine a garden hose spraying pure water — bring a magnet near the stream and nothing happens, because water is electrically neutral. But if that stream carried electric charge (a current), the magnet would push the whole stream sideways. That is the essence of this concept: a current-carrying wire placed in a magnetic field experiences a sideways force, because every moving charge inside the wire feels the Lorentz force, and since the charges cannot leave the wire, they drag the wire along with them.

From a single charge to a wire

A single charge $q$ moving with velocity $\vec v$ in a field $\vec B$ feels $\vec F = q(\vec v \times \vec B)$. A current is just many such charges drifting together, so summing their individual forces over the whole wire gives a net force on it.

The formula

For a straight wire of length $L$ carrying current $I$ in a uniform field $\vec B$:

where $\vec L$ points along the current and $\theta$ is the angle between the wire and $\vec B$.

Direction: the right-hand rule

Point your index finger along the current ($\vec L$), your middle finger along the field ($\vec B$); your thumb then gives the force direction — this is just the cross product $\vec L \times \vec B$ read off by hand. Because it is a cross product, swapping the two vectors reverses the force.

Worked example

A $0.5\ \text{m}$ wire carries $3\ \text{A}$ from east to west, in a uniform field of $0.2\ \text{T}$ pointing north.

• $\theta = 90^\circ$ (the wire and the field are perpendicular), so $F = ILB\sin\theta = (3)(0.5)(0.2)(1) = 0.3\ \text{N}$.
• Direction: index finger west (current), middle finger north (field) — curling from west to north, the right-hand thumb points vertically downward. (Flip it: current flowing east with the same northward field gives a force straight up — reversing the current direction always reverses the force.)

Why it matters

This is the operating principle behind electric motors (opposite sides of a current loop feel opposite forces, producing rotation), galvanometers (a current-carrying coil deflects in a fixed field), and loudspeakers (a current-carrying voice coil is pushed back and forth by a magnet). It is not a new force — it is the same Lorentz force acting on the charges inside the wire, transmitted to the wire as a whole.

Queries like "force on current carrying conductor in magnetic field formula" and "moving charges and magnetism class 12 numericals" point to the Moving Charges and Magnetism chapter of the NCERT/CBSE Class 12 Physics curriculum. This same result underlies electric-motor and galvanometer questions commonly tested in JEE Main and NEET.