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medium difficulty9 min

Force Between Two Parallel Current-Carrying Wires

Two long parallel current-carrying wires exert magnetic forces on each other because each wire lies in the magnetic field produced by the other. The force per unit length is F/l = μ0 I1 I2/(2π d).

In one line: Parallel currents act like partners when same, opponents when opposite.

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Understand it

  • A current in the first wire produces a magnetic field at the position of the second wire.
  • The second wire carrying current in this field experiences a force.
  • Currents in the same direction attract, while currents in opposite directions repel.
  • This interaction is also connected with the SI definition of ampere in the school-level treatment.

Example

Two overhead conductors carrying currents in the same direction attract each other magnetically. If the currents are reversed relative to each other, the force becomes repulsive.

Formula and rule

F/l = μ0 I1 I2/(2π d).

I1 and I2 are currents in ampere, d is separation in metre, F/l is in N m−1.

Same-direction currents attract; opposite-direction currents repel.

Assumes long, straight, parallel wires separated by distance d in air or vacuum approximation.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

Two long parallel wires 0.05 m apart carry 10 A and 20 A in the same direction.

  1. 1F/l = (4π x 10−7 × 10 × 20)/(2π x 0.05) = 8.0 × 10−4 N m−1.
  2. 2Since currents are in the same direction, the force is attractive.

Method you can reuse

  1. 1Find I1, I2, and d in SI units.
  2. 2Substitute in F/l = μ0 I1 I2/(2π d).
  3. 3Simplify powers of ten carefully.
  4. 4Decide attraction or repulsion from current directions.
  5. 5State the final value with N m−1.

Visual tip

A simple two-wire diagram should show currents I1 and I2, separation d, magnetic field due to one wire at the other, and force arrows. Though not always mandatory, it prevents direction errors.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

What happens to the force between two parallel wires if both currents are doubled and distance is unchanged?

Think first, then show answer
The force per unit length becomes four times because F/l is directly proportional to I1 I2. Doubling both currents changes the product from I1 I2 to 4I1 I2.

Common wrong answer

Writing force in newton without multiplying by length when only F/l is calculated is incomplete for questions asking total force on a given length.

Don't mix this up

Students often write only the magnitude formula and forget to state whether the force is attractive or repulsive.

Exam tip

After calculating force per unit length, always add the nature of force. Direction carries marks in conceptual and assertion-reason questions.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Asked as a direct numerical, a reason for attraction or repulsion, or a definition-based question related to ampere.
  1. 1

    Enough for 1 mark

    Two long parallel current-carrying wires exert magnetic forces on each other because each wire lies in the magnetic field produced by the other. The force per unit length is F/l = μ0 I1 I2/(2π d).

  2. 2

    Add for 2 marks

    Example: Two overhead conductors carrying currents in the same direction attract each other magnetically. If the currents are reversed relative to each other, the force becomes repulsive.

  3. 3

    Add for 3 marks

    A current in the first wire produces a magnetic field at the position of the second wire.

Practice

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