ScienceCBSE Class 10 · Magnetic Effects of Electric Current

Magnetic Field due to a Current-Carrying Circular Loop and Solenoid

Updated 14 October 2026 · Fact-checked

A current-carrying circular loop produces field lines that are concentric circles near the wire and nearly straight at the centre, all pointing the same way inside the loop. A solenoid, a long coil of many turns, produces a field like a bar magnet, with uniform, parallel field lines inside. Placing soft iron inside it makes an electromagnet.

Understand Magnetic Field due to Circular Loop and Solenoid

Starting point: a straight wire. A current in a straight wire produces magnetic field lines that are concentric circles centred on the wire. The right-hand thumb rule gives their direction: hold the wire in your right hand with the thumb along the current; your fingers curl in the direction of the field lines. The field is stronger for a larger current and weaker farther from the wire.

Circular loop. Now bend the wire into a circle. Near each part of the wire the field lines are small concentric circles. Moving away from the wire, the circles grow larger. By the time we reach the centre of the loop, these large circles look like straight lines. Applying the right-hand thumb rule to every small section shows that all sections produce field in the same direction inside the loop, so their effects add.

The field at a point depends directly on the current, so a larger current gives a stronger field.
For a coil of n turns, the current in each turn has the same direction, so the field is n times that of a single turn.
A quick way to find which face behaves like which pole (a standard aid, consistent with the right-hand rule): looking at a face of the loop, if the current flows anticlockwise, that face acts as a north pole; if clockwise, a south pole.

Solenoid. Wind insulated copper wire into many close circular turns forming a cylinder and you have a solenoid. Its field pattern is very like that of a bar magnet:

one end behaves as a north pole and the other as a south pole;
inside, the field lines are parallel straight lines, showing that the field is the same at all points inside: it is uniform;
outside, the lines spread from one end and return to the other, just like a bar magnet's.

The field inside a solenoid becomes stronger if the current is increased or if there are more turns.

Electromagnet. The strong field inside a solenoid can magnetise a piece of magnetic material such as soft iron placed inside the coil. This is an electromagnet: a soft iron core wrapped with a coil of insulated copper wire. Unlike a bar magnet, its magnetism can be switched on and off with the current, and its strength can be changed by changing the current or number of turns; reversing the current reverses its poles.

Properties of field lines (recap). Field lines emerge from the north pole and merge at the south pole outside a magnet, and run from south to north inside, forming closed curves. Crowded lines mean a stronger field. Two field lines never cross, because a compass at the crossing point would have to point in two directions at once.

Magnetic Field due to Circular Loop and Solenoid: formulas and key facts

Right-hand thumb rule: $thumb ∥ current \Rightarrow curled fingers = field direction$; Also called Maxwell's corkscrew rule.
Coil of n turns: $B_{coil} = n \times B_{one turn}$; Field adds because current in every turn flows the same way.
Factors increasing field of a coil or solenoid: $larger current, more turns$; A soft iron core makes an electromagnet.
Field inside a long solenoid: $uniform: parallel, equally spaced lines$; Same at all points inside.

How to solve Magnetic Field due to Circular Loop and Solenoid questions

For questions on loops and solenoids, use the right-hand thumb rule section by section.

1Mark the direction of current in the loop or turns.
2Apply the right-hand thumb rule to one side of the loop and find the field direction inside the loop; it is the same for every section.
3Decide the poles: the face where field lines come out acts as north (anticlockwise current seen from that face).
4For a solenoid, the end out of which field lines leave is north; the other end is south.
5For 'how to make the field stronger', list: increase current, increase number of turns, add a soft iron core.
6When drawing, show concentric circles near the wire, straight lines at the centre of a loop, and parallel lines inside a solenoid with arrows.

Magnetic Field due to Circular Loop and Solenoid in real life

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

Electromagnet

Suppose a scrap-yard crane uses a large electromagnet to lift iron scrap from one heap and drop it onto a truck.

Explain how the crane's electromagnet works, why soft iron is used for its core, how the operator releases the scrap, and two ways to lift heavier loads.

Try it first, then show the solutionSolution

The electromagnet is a soft iron core wrapped with a coil of insulated copper wire (a solenoid around iron).
When current flows, the uniform strong field inside the solenoid magnetises the soft iron core, which attracts the iron scrap.
To release the scrap, the operator switches off the current; the field disappears and soft iron loses its magnetism, so the scrap drops.
To lift heavier loads, increase the current through the coil or increase the number of turns.

Answer: Current through the coil magnetises the soft iron core; switching off releases the load; more current or more turns makes it stronger.

Memory hook: Switch on to grab, switch off to drop: an electromagnet obeys the current.

Tricks to remember Magnetic Field due to Circular Loop and Solenoid

Short memory aids. Say each one aloud once, then use it on a question the same day.

Clock rule for poles
Looking at a face: current Clockwise = South, Anticlockwise = North (draw S and N with arrows on their tips).
Use it when: Finding the poles of a loop or solenoid.
Thumb with the current
Right thumb along the current, fingers show the field.
Use it when: Field around a wire or loop.
Solenoid = bar magnet in a coil
Outside like a bar magnet; inside straight and uniform.
Use it when: Drawing solenoid field lines.

Magnetic Field due to Circular Loop and Solenoid: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Loop on a table · 2 marks · Very short answerBoard level

A circular loop lies in the plane of a table and current flows through it clockwise (seen from above). Use the right-hand thumb rule to find the direction of the magnetic field inside and outside the loop.

Try it first, then show the solutionSolution

Hold any part of the wire with the right thumb along the clockwise current; the fingers curl into the table inside the loop (1 mark).
So the field is perpendicular to the table, pointing into the table (downwards) inside the loop and out of the table (upwards) outside it (1 mark).

Answer: Inside: into the table; outside: out of the table.

Example 2: Field pattern of a loop · 3 marks · Short answerHarder board level

Draw the pattern of magnetic field lines of a current-carrying circular loop and explain why the field lines near the centre are almost straight. How does the field change if the loop is replaced by a coil of 50 turns carrying the same current?

Try it first, then show the solutionSolution

Diagram: small concentric circles around each side of the wire, growing larger towards the centre, with straight lines through the centre; arrows consistent with the current (1 mark).
The circles from each part of the wire become larger farther from the wire; at the centre their arcs are so large that they look like straight lines, and every section contributes in the same direction (1 mark).
With 50 turns carrying the same current, each turn's field adds, so the field becomes 50 times as large (1 mark).

Answer: Concentric circles near the wire, straight lines at the centre; field becomes 50 times stronger with 50 turns.

Example 3: Solenoid vs bar magnet · 5 marks · Long answerHarder board level

(a) What is a solenoid? (b) Draw its field lines and compare with a bar magnet. (c) What do parallel field lines inside a solenoid indicate? (d) State two ways to increase the strength of its field.

Try it first, then show the solutionSolution

(a) A coil of many circular turns of insulated copper wire wound closely in the shape of a cylinder (1 mark).
(b) Field lines: parallel straight lines inside; outside, they leave one end and curve round to enter the other, like those of a bar magnet; one end acts as N, the other as S (1½ marks).
(c) The field is uniform: the same at all points inside (1 mark).
(d) Increase the current; increase the number of turns (also: place a soft iron core inside) (1½ marks).

Answer: (a) Closely wound cylindrical coil. (b) Like a bar magnet. (c) Uniform field. (d) More current, more turns.

Example 4: Find the poles · 3 marks · Short answerHOTS / competency

A solenoid is held horizontally. Seen from its right-hand end, the current in the turns flows anticlockwise. (a) Which end is the north pole? (b) A compass is placed beyond the right-hand end on the axis. Which way does its north pole point? (c) What happens to these answers if the battery connections are reversed?

Try it first, then show the solutionSolution

(a) Anticlockwise current seen from the right end means that end acts as a north pole (field lines come out of it) (1 mark).
(b) Outside the solenoid, field lines leave the north end; the compass's north pole points along the field, away from the solenoid (1 mark).
(c) Reversing the current makes the right end a south pole; the compass's north pole then points towards the solenoid (1 mark).

Answer: (a) Right end is N. (b) Away from the solenoid. (c) Poles reverse; compass points towards it.

Example 5: Electromagnet vs permanent magnet · 3 marks · Short answerHarder board level

Give three differences between an electromagnet and a permanent bar magnet. Why is soft iron, rather than steel, preferred for the core of an electromagnet used in a crane?

Try it first, then show the solutionSolution

An electromagnet's magnetism can be switched on and off; a bar magnet's cannot (1 mark).
An electromagnet's strength can be changed by changing the current or number of turns; its poles can be reversed by reversing the current. A bar magnet's strength and poles are fixed (1 mark).
Soft iron is magnetised strongly while current flows and loses its magnetism when the current stops, so the crane can release its load; steel would stay magnetised (1 mark).

Answer: Switchable, adjustable strength, reversible poles; soft iron loses magnetism when current stops.

Where students lose marks in Magnetic Field due to Circular Loop and Solenoid

The slips examiners see most often, and what to write instead.

Mistake: Using the left hand for field direction
Confusion with Fleming's left-hand rule.
Wrong working
Left thumb along the current gives the field.
Right working
Right-hand thumb rule for the field of a current; Fleming's left-hand rule for force.
Do this: Right for field, left for force.
Usually costs: 1-2 marks.
Mistake: Drawing curved or converging lines inside a solenoid
Students copy the outside pattern.
Wrong working
Lines inside bending towards the ends.
Right working
Parallel, equally spaced straight lines inside.
Do this: Inside is uniform.
Usually costs: 1 mark in diagrams.
Mistake: Missing arrows on field lines
Students draw patterns only.
Wrong working
Concentric circles without arrows.
Right working
Arrows showing direction, consistent with the right-hand thumb rule.
Do this: Always add arrows.
Usually costs: ½ to 1 mark.
Mistake: Saying a steel core is best for an electromagnet
Steel is associated with strength.
Wrong working
Steel core makes the best switchable electromagnet.
Right working
Soft iron is used; it loses magnetism when the current stops.
Do this: Soft iron for switchable; steel for permanent magnets.
Usually costs: 1 mark.

Exam tips

Practise drawing field lines of a straight wire, a loop and a solenoid with correct arrows.
Always name the rule (right-hand thumb rule) when finding field direction.
For the strength of the field, mention both current and number of turns.
Use the phrase 'uniform magnetic field' for the inside of a solenoid.
Electric motor and generator are formative-only in 2026-27; they are not asked in the board exam.

Practice questions on Magnetic Field due to Circular Loop and Solenoid

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

Q1 · 1 mark · MCQBoard level
The magnetic field inside a long straight current-carrying solenoid:
(a) is zero (b) decreases towards its ends (c) increases towards its ends (d) is the same at all points
Hint
Parallel lines inside.
Answer
(d) is the same at all points (uniform).
Q2 · 1 mark · Assertion-reasonBoard level
Assertion (A): A current-carrying solenoid behaves like a bar magnet.
Reason (R): One end of a current-carrying solenoid behaves as a north pole and the other as a south pole.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Hint
Compare the field patterns.
Answer
(a).
Q3 · 2 marks · Very short answerHarder board level
Draw a diagram to represent a uniform magnetic field in a region. Where is such a field found in the case of a current-carrying conductor?
Hint
Equally spaced parallel lines.
Answer
Equally spaced parallel straight lines, all with arrows in the same direction. Such a field exists inside a long current-carrying solenoid.
Q4 · 4 marks · Case-basedHOTS / competency
Read the passage and answer.
Suppose a student winds 100 turns of insulated copper wire on a cardboard tube, connects it to a battery through a rheostat, and slides an iron nail into the tube. The nail then picks up 6 small pins. When she doubles the current, it picks up more pins.
(a) What device has she made? (1 mark)
(b) Why does the nail attract pins only while current flows? (1 mark)
(c) Give two more changes she could make to pick up more pins, and explain why each works. (2 marks)
Hint
Field of a solenoid depends on current and turns.
Answer
(a) An electromagnet. (b) The field inside the current-carrying coil magnetises the iron nail; when the current stops, the field disappears and the nail (soft iron) loses most of its magnetism. (c) Increase the number of turns (each turn adds its field) and increase the current further (field depends directly on current); a thicker soft iron core also helps.
Q5 · 3 marks · Short answerHOTS / competency
Two identical circular loops lie side by side on a table. In loop A the current flows clockwise; in loop B, anticlockwise (seen from above). State the direction of the field at the centre of each loop, and predict what you would find at the centre if one loop were placed exactly on top of the other with these currents.
Hint
Fields in opposite directions cancel.
Answer
A (clockwise): field into the table at its centre. B (anticlockwise): field out of the table. If stacked, their equal and opposite fields at the centre would cancel, giving nearly zero field.
Q6 · 3 marks · Short answerBoard level
List three properties of magnetic field lines and explain why two field lines never intersect.
Hint
Direction, closeness, closed curves.
Answer
(1) Outside a magnet they go from north to south, inside from south to north, forming closed curves. (2) They are crowded where the field is strong. (3) They never cross. If two lines crossed, a compass at that point would have to point in two directions at once, which is impossible.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1.Shape of field lines around a straight wire?Show answer
Concentric circles centred on the wire.
2.Field at the centre of a loop looks like?Show answer
Straight lines.
3.Field due to a coil of n turns?Show answer
n times that of one turn.
4.What is a solenoid?Show answer
A coil of many turns of insulated copper wire wound closely in a cylinder.
5.Field inside a solenoid?Show answer
Uniform (same at all points).
6.What is an electromagnet?Show answer
A soft iron core magnetised by the field of a current-carrying coil.

Magnetic Field due to Circular Loop and Solenoid: frequently asked questions

What does the magnetic field of a solenoid look like?

Like that of a bar magnet outside, with one end north and the other south; inside, the lines are parallel and straight, showing a uniform field.

How can the magnetic field of a coil be increased?

By increasing the current through it, increasing the number of turns, or placing a soft iron core inside.

Why are the field lines straight at the centre of a circular loop?

The concentric circles around each part of the wire become very large at the centre, so their arcs look straight, and all parts of the loop add their fields in the same direction there.

What is the right-hand thumb rule?

If you hold a current-carrying conductor in your right hand with the thumb along the current, your curled fingers show the direction of the magnetic field lines.

Are the electric motor and generator in the board syllabus?

No. In 2026-27 the motor, electromagnetic induction and the generator are assessed only formatively.