Moving Charges and Magnetism — Part 2: Forces and torques on currents; the galvanometer: visual lesson, CBSE Class 12 Physics

Lesson

Forces and torques on currents

Part 2 — the push on a wire in a magnetic field, the pull between two currents, and the turning effect that makes meters and motors work.

In this lesson you will

Find the force on a current-carrying conductor and between two parallel currents; define the ampere
Calculate the torque on a current loop and treat it as a magnetic dipole
Explain the moving coil galvanometer and its conversion into an ammeter and a voltmeter

Concept

Force on a current-carrying conductor

Adding the forces $q\vec v_d \times \vec B$ on all the drifting charges in a straight conductor of length $l$ : $\vec F = I\,\vec l \times \vec B,\qquad F = IlB\sin\theta$ where $\vec l$ points along the current.

Largest when the wire is perpendicular to $\vec B$ ; zero when parallel.
Direction: perpendicular to both the wire and the field (Fleming’s left-hand rule gives the same answer).

Table: the force on a wire is zero parallel to the field, I l B sine theta at an angle and largest perpendicular
Wire relative to B	Force
Parallel	0
At angle θ	IlB sin θ
Perpendicular	IlB (largest)

Diagram

Force between two parallel currents

Wire 1 makes a field $B_1 = \dfrac{\mu_0 I_1}{2\pi d}$ at wire 2. The force on a length $L$ of wire 2 is $I_2 L B_1$ , so the force per unit length is $\dfrac{F}{L} = \dfrac{\mu_0 I_1 I_2}{2\pi d}$ Like currents attract; opposite currents repel.

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