Chapter 12 · Question 5

How does the magnetic field pattern of a current-carrying circular loop differ from that of a straight wire? What is a solenoid, and how does its magnetic field compare with that of a bar magnet? Why is the field inside a solenoid uniform?

Answer Revealed

Direct Answer:

For a straight wire, the field lines are concentric circles centred on the wire. For a circular loop, every section of the wire produces concentric circles that become larger towards the centre. At the centre of the loop, the arcs of these large circles appear as straight lines, and every section of the wire contributes to the field in the same direction within the loop — so the field lines near the centre are parallel. A solenoid is a coil of many circular turns of insulated copper wire wrapped closely in the shape of a cylinder. Its magnetic field pattern is similar to that of a bar magnet: one end behaves as a north pole and the other as a south pole, and field lines are closed curves. Inside a solenoid, the field lines are parallel straight lines, indicating that the field is the same at all points — that is, the field is uniform. If there are

n

turns, the field is

n

times that of a single turn because the current in each turn has the same direction and the fields add up.

Simple Explanation

A straight wire gives you circles around it. Bend that same wire into a loop, and the circles from all sides of the loop converge — the field at the centre becomes straight and uniform, and the loop acts like a tiny flat magnet with a north and south side. Now take many such loops, stack them tightly into a cylinder, and you have a solenoid. A solenoid is basically an artificial bar magnet. Outside, the field lines look just like a bar magnet's — they emerge from one end (north) and curve around to the other (south). Inside, the field lines run straight and parallel, meaning the field strength is the same everywhere inside. Each turn of wire contributes to the field, so more turns mean a stronger magnet.

Exam-Ready Structure

The magnetic field of a current-carrying conductor depends on the shape of the conductor — circular loops and solenoids produce distinctly different patterns from a straight wire. 1. Circular loop vs straight wire: (a) For a straight wire, magnetic field lines are concentric circles centred on the wire. (b) For a circular loop, at every point on the loop the concentric circles representing the magnetic field become larger as we move towards the centre. (c) At the centre of the loop, the arcs of these large circles appear as straight lines. By applying the right-hand rule, every section of the wire contributes to the magnetic field in the same direction within the loop. 2. Multiple turns: The magnetic field produced by a current-carrying wire at a given point depends directly on the current passing through it. For a circular coil with

n

turns, the field produced is

n

times as large as that produced by a single turn, because the current in each circular turn has the same direction and the fields add up. 3. Solenoid definition: A coil of many circular turns of insulated copper wire wrapped closely in the shape of a cylinder is called a solenoid. 4. Solenoid field vs bar magnet: (a) The pattern of magnetic field lines around a current-carrying solenoid (Fig. 12.10) is similar to that of a bar magnet. (b) One end of the solenoid behaves as a magnetic north pole and the other behaves as a south pole. (c) The field lines are closed curves, entering one end (south pole) and emerging from the other (north pole), exactly like a bar magnet. 5. Uniform field inside a solenoid: The field lines inside the solenoid are in the form of parallel straight lines. This indicates that the magnetic field is the same at all points inside the solenoid — that is, the field is uniform. By contrast, the field outside is non-uniform and weaker.

Key Points

Circular loop: field lines at centre are parallel straight lines; contributes in same direction
For $n$ turns: magnetic field is $n$ times that of a single turn (fields of each turn add up)
Solenoid: coil of many circular turns wrapped closely in a cylinder shape
Solenoid's magnetic field pattern is similar to that of a bar magnet (north and south poles, closed curves)
Inside a solenoid: field lines are parallel straight lines → uniform magnetic field

How does the magnetic field pattern of a current-carrying circular loop differ from that of a straight wire? What is a solenoid, and how does its magnetic field compare with that of a bar magnet? Why is the field inside a solenoid uniform?