Magnetic Effects of Electric Current · Lesson 4 of 8
Magnetic Field due to a Current through a Circular Loop
“Bend the wire into a loop and all its tiny magnetic contributions start cooperating.”
• Describe the magnetic-field pattern produced by a current-carrying circular loop. • Explain why contributions from different parts of the loop reinforce one another at the centre. • Apply the Right-Hand Thumb Rule to clockwise and anticlockwise loop currents. • Predict how current and the number of turns affect field strength. • Interpret iron-filing patterns around a circular coil. • Solve direction and comparison problems involving circular loops.
A straight wire produces circular magnetic field lines around itself. If the wire is bent into a loop, every small section still produces a field, but the fields from the different sections now overlap. At the centre of the loop, these contributions point in the same direction and reinforce one another.
Close to any small portion of the wire, the field lines resemble circles around a straight conductor. As one moves towards the centre of the loop, the circular arcs produced by opposite sections become larger and appear nearly straight. The combined field near the centre is therefore represented by nearly parallel lines passing perpendicular to the plane of the loop.
Use the Right-Hand Thumb Rule on each section of the loop or use a compact loop version: curl the fingers of the right hand in the direction of conventional current around the loop; the extended thumb then points along the field through the centre. An anticlockwise current as seen by an observer produces a field towards that observer, while a clockwise current produces a field away from the observer.
A field emerging from the page is often represented by a dot, like the tip of an approaching arrow. A field entering the page is represented by a cross, like the tail of an arrow moving away.
Field direction inside and outside the loop must not be treated as identical. Field lines are closed curves: they pass through the centre in one direction, bend around outside the loop and return in the opposite direction. Thus, if the central field comes out of the page, the returning external field goes into the page.
The magnetic field at a given point becomes stronger when current increases. It also becomes stronger when the coil contains more turns. In an n-turn coil, the same current flows in the same sense through each turn, so the fields produced by all turns add. Under the same conditions, the field of n identical turns is n times the field of one turn.
| Change to the coil | Effect at the same observation point | Reason |
|---|---|---|
| Increase current | Stronger field | Each wire section produces a stronger field |
| Reverse current | Field direction reverses | Every section reverses its contribution |
| Increase number of turns | Stronger field | Fields from the turns add |
| Move away from the loop | Weaker field | The field spreads through a larger region |
Activity
Insert a circular coil with many turns through two holes in a rectangular cardboard so that the coil is normal to the cardboard. Connect the coil in series with a battery, key and rheostat. Sprinkle iron filings uniformly, close the key briefly and tap the cardboard gently. The filings arrange in a pattern that reveals the field around the coil.
Near the wire the filings form curved patterns associated with individual sections. Near the central region, the pattern shows the reinforcing direction of the field. Reversing the battery reverses the direction but not the general shape of the pattern. Increasing current or turns strengthens the field without changing the basic geometry of the coil.
Identify how the current appears to the stated observer. Curl the right-hand fingers in that direction. The thumb gives the central field: towards the observer for anticlockwise current and away from the observer for clockwise current. Then reverse the direction outside the loop because field lines return as closed curves.
Problem
Current in a circular loop appears clockwise to an observer looking at the page. Find the magnetic-field direction at the centre.
- 1.Given: the visible current is clockwise.
- 2.Curl the fingers of the right hand clockwise.
- 3.The right thumb points away from the observer, into the page.
- 4.Therefore the central field is into the page and can be represented by a cross.
Problem
Two identical circular coils carry the same current. Coil A has one turn and coil B has five turns. Compare their central fields.
- 1.Given: shape, current and observation point are the same; only turn count differs.
- 2.For identical turns, the contributions reinforce and Bₙ = nB₁.
- 3.Coil B has five turns, so its field is 5B₁.
- 4.Coil B therefore produces five times the central field of coil A.
- 5.Their directions are the same if their currents circulate in the same sense.
Problem
A six-turn coil carries current anticlockwise. The current is reversed and its magnitude is doubled. Compare the new central field with the original field.
- 1.The number of turns remains six, so the turn factor does not change.
- 2.Doubling current doubles the magnitude of the field.
- 3.Reversing current reverses the field direction.
- 4.Thus the new field is twice as strong but points opposite to the original field.
- 5.Because the original current was anticlockwise, its field was out of the page; the new field is into the page.
The field at the centre is not produced by only the nearest part of the wire. Every section contributes. Symmetry makes sideways components cancel, while components perpendicular to the loop reinforce in one central direction.
Quiz
What is the field direction at the centre of an anticlockwise current loop as seen by an observer?
Why do different sections of a circular loop reinforce the central field?
What happens if the number of identical turns is doubled while current stays fixed?
How do field lines behave outside the loop?
A clockwise loop current is reversed. What happens to the central field?
Practice Problems
- A loop current appears anticlockwise. State the central field direction. Answer: Curling the right-hand fingers anticlockwise makes the thumb point towards the observer, so the central field is out of the page.
- Explain why the field lines near the centre appear nearly straight. Answer: The circular arcs produced by different wire sections become large near the centre. Their reinforcing portions are nearly parallel and therefore appear as straight lines over the small central region.
- A single-turn coil produces field B at its centre. Find the field of a four-turn identical coil carrying the same current. Answer: Bₙ = nB₁ = 4B. The direction remains the same if current circulates in the same sense.
- A four-turn coil carrying current I is replaced by an eight-turn coil carrying half the current. Compare the central fields under otherwise identical conditions. Answer: Field is proportional to turns multiplied by current. Original factor is 4I; new factor is 8 × I/2 = 4I, so the fields are equal in magnitude.
- Current is clockwise and the central field is into the page. Describe the external return field. Answer: Magnetic field lines are closed curves, so after passing into the page through the central region, they curve around outside and return out of the page.
Key Takeaways
• Every section of a current-carrying circular loop contributes to its magnetic field. • At the centre, the field contributions reinforce and are nearly parallel. • Anticlockwise current produces a central field towards the observer; clockwise current produces one away. • Reversing current reverses the complete field direction. • Increasing current strengthens the field. • For identical turns, an n-turn coil produces n times the field of one turn under the same conditions. • Magnetic field lines pass through the loop and return outside as closed curves.