Magnetic effects of current — right hand rule, solenoid, toroid field patterns

Question

How do we determine the direction of magnetic field around a straight wire, a solenoid, and a toroid? Explain the right-hand rules for each case.

(CBSE 10/12 + JEE Main + NEET)

Solution — Step by Step

Wrap your right hand around the wire with the thumb pointing in the direction of current. Your curled fingers show the direction of the magnetic field.

The field lines form concentric circles around the wire. Field magnitude:

B = \frac{\mu_0 I}{2\pi r}

where $r$ is the perpendicular distance from the wire.

Curl your right hand fingers in the direction of current flow through the coil. Your thumb points toward the North pole (direction of field inside the solenoid).

Inside a solenoid, the field is uniform: $B = \mu_0 n I$

where $n$ = number of turns per unit length and $I$ = current.

A toroid is a solenoid bent into a doughnut shape. The field exists ONLY inside the ring:

B = \mu_0 n I = \frac{\mu_0 N I}{2\pi r}

where $N$ = total turns, $r$ = radius of the toroid ring.

Outside the toroid, $B = 0$ — the field is completely contained. This makes toroids useful in transformers and inductors.

Use the right hand rule for force: point fingers along current $I$ , curl them toward $B$ . The thumb gives the direction of force $\vec{F}$ .

F = BIL\sin\theta

where $\theta$ is the angle between the wire and the field.

flowchart TD
    A["Find magnetic field direction"] --> B{"What geometry?"}
    B -- "Straight wire" --> C["Right Hand Thumb Rule"]
    C --> D["Thumb = current, Fingers = field circles"]
    B -- "Solenoid" --> E["Curl fingers along current"]
    E --> F["Thumb = North pole = B inside"]
    B -- "Toroid" --> G["Same as solenoid but closed loop"]
    G --> H["B only inside the ring"]
    A --> I{"Find force direction?"}
    I --> J["F = BIL sinθ"]
    J --> K["Right hand: fingers from I toward B, thumb = F"]

Why This Works

A moving charge creates a magnetic field (this is a fundamental fact of nature described by Maxwell’s equations). The right-hand rules are just convenient ways to encode the cross product $\vec{F} = q\vec{v} \times \vec{B}$ , which naturally produces a direction perpendicular to both the velocity and the field.

A solenoid concentrates the field inside because the fields from adjacent coils add up inside and cancel outside. A toroid takes this further — by closing the loop, there is NO outside, so the field is perfectly contained.

Alternative Method

Instead of the right-hand rule, you can use clock rule for solenoids: look at the end of the solenoid. If current flows anticlockwise, that end is North. If clockwise, that end is South. Think of it as: anticlockwise = N (like the letter N which has strokes going anticlockwise), clockwise = S.

For CBSE 10, you only need the right-hand thumb rule for straight wires and the solenoid rule. For CBSE 12 and JEE, you also need Biot-Savart law and Ampere’s circuital law. The solenoid field formula $B = \mu_0 nI$ is derived using Ampere’s law — know the derivation for boards.

Common Mistake

Students confuse the right-hand rule for field direction with the right-hand rule for force direction. For a straight wire, curl fingers to find field. For force on a wire in a field, use the cross product (fingers from $I$ toward $B$ , thumb gives $F$ ). Mixing these up gives the wrong direction. Label which rule you are using before applying it.

Question

Solution — Step by Step

Why This Works

Alternative Method

Common Mistake

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