Magnetic field of a straight wire: right-hand rule, compass needles and force between wires

Compass needles around a long straight current show circular field lines with B = μ₀I/2πr. Reverse the current, add a second wire (same or opposite direction) and see the combined field and the force between the wires that defines the ampere.

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About this experiment

Aim

To see that a long straight current produces a magnetic field in circles around it, to find its direction by the right-hand rule and its size from B = μ₀I/2πr, and to find the force between two parallel wires.

Theory

Oersted (1820) saw that a compass needle near a wire carrying a current turns. The field lines are circles around the wire, in planes at right angles to it. Right-hand rule: grasp the wire with the right hand with the thumb along the current; the fingers curl in the direction of B.

Ampere's circuital law ∮ B·dl = μ₀ I with a circle of radius r around the wire gives B × 2πr = μ₀ I, so B = μ₀ I / 2πr. The field falls as 1/r. Here μ₀ = 4π × 10⁻⁷ T·m/A. A current of 5 A gives 10 µT at 10 cm, about a fifth of the Earth's magnetic field.

Two parallel wires: wire 2 lies in the field of wire 1, so it feels a force F = B₁ I₂ L. Per unit length F/L = μ₀ I₁ I₂ / 2π d. Currents in the same direction attract each other, currents in opposite directions repel. This force defines the ampere: 1 A is the current which, in two long parallel wires 1 m apart, gives a force of 2 × 10⁻⁷ N per metre of length.

Formulas used

• B = μ₀ I / (2π r)
• μ₀ = 4π × 10⁻⁷ T m A⁻¹
• ∮ B · dl = μ₀ I (Ampere's circuital law)
• force per unit length F/L = μ₀ I₁ I₂ / (2π d)
• right-hand rule: thumb = current, fingers = field

Procedure: what to do in the virtual lab

1. With one wire (5 A) look at the needles. Check that they form circles and use the right-hand rule for the direction.
2. Move the probe to different r and check B = μ₀I/2πr: at 10 cm it should be 10 µT.
3. Reverse the current: the needles turn round.
4. Add a second wire with the current in the same direction. Find the point where B = 0. Read the force per metre and note that it is attractive.
5. Reverse the second current and see what changes in the field and in the force.

Observations to make

• The needles point along circles around the wire, never towards or away from it.
• B halves when the distance doubles.
• Equal parallel currents attract; opposite currents repel.
• Between two equal currents in the same direction there is a line where the field is zero.

What you can change in this experiment

• Current in wire 1 (1 to 20 A)
• Direction of the current in wire 1: out of the page (towards you) / into the page (away from you)
• Wires: one wire / two wires, currents in the same direction / two wires, currents in opposite directions
• Distance between the wires (two-wire modes) (4 to 16 cm)
• Distance of the probe point from wire 1 (1 to 16 cm)

Viva questions on Magnetic field of a straight wire

Questions an examiner may ask in the Class 12 physics practical. Run the experiment in the lab to find the answers yourself, then check them in the Learn tab.

1. State Ampere's circuital law.
2. How does the magnetic field of a long straight wire vary with distance?
3. Do two parallel wires with currents in the same direction attract or repel?
4. How is the ampere defined?

Frequently asked questions

Syllabus: Class XII Physics, Chapter 4 — Moving Charges and Magnetism, §4.3 (Biot–Savart), §4.5 (Ampere's circuital law), §4.7 (force between two parallel currents)

What you do in the lab

Change the controls and watch the physics behave in real time in 3D. Live readouts and graphs show the numbers behind it, and the Learn tab has the theory, procedure, observations and viva questions. Works on a phone or a laptop, in English and Hindi.

Topics: magnetic field of a straight wire · right hand rule · Ampere's circuital law · force between parallel wires · definition of ampere · oersted experiment · moving charges and magnetism

Read the full guide: Moving charges and magnetism.

More from this chapter

• Force between parallel current-carrying wires
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• Charged particle in uniform E and B fields
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• Force on a current-carrying rod in a magnetic field: rod on rails and Fleming's left-hand rule
• Galvanometer to ammeter and voltmeter
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