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Question:

Two long straight parallel wires, carrying (adjustable) current I1 and I2, are kept at a distance d apart. If the force 'F' between the two wires is taken as 'positive' when the wires repel each other and 'negative' when the wires attract each other, the graph showing the dependence of 'F' on the product I1I2 would be?

Solution:

The force between two wires per unit length is: F = μ₀/(2πd)I₁I₂

Where:

  • F is the force per unit length between the wires.
  • μ₀ is the permeability of free space (a constant).
  • d is the distance between the wires.
  • I₁ and I₂ are the currents in the two wires.

The equation shows that the force F is directly proportional to the product I₁I₂. If I₁ and I₂ have the same sign (both positive or both negative, meaning currents flow in the same direction), the force F is positive (repulsion). If I₁ and I₂ have opposite signs (one positive, one negative, meaning currents flow in opposite directions), the force F is negative (attraction). Therefore, the graph of F versus I₁I₂ will be a straight line passing through the origin with a positive slope.