Three parallel wires each carry current I in the directions shown in (Figure 1). The separation between adjacent wires is d.
a) Calculate the magnitude of the net magnetic force per unit length on the top wire.
b) Calculate the magnitude of the net magnetic force per unit length on the middle wire.
c) Calculate the magnitude of the net magnetic force per unit length on the bottom wire.

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onyebuchinnaji onyebuchinnaji · Answer 1 · 2022-07-21T20:04:14+02:00

(a) The magnitude of the net magnetic force per unit length on the top wire is μI²/πd.

(b) The magnitude of the net magnetic force per unit length on the middle wire is zero.

(c) The magnitude of the net magnetic force per unit length on the bottom wire is 3μI²/4πd.

The magnitude of the net magnetic force per unit length on the top wire is calculated as follows;

F₁/L = (μI₁/2π) x (I₂/d + I₃/d)

F₁/L = (μI/2π) x (I/d + I/d)

F₁/L = (μI/2π) x (2I/d)

F₁/L = μI²/πd

The magnitude of the net magnetic force per unit length on the middle wire is calculated as follows;

F₂/L = (μI₂/2π) x (I₃/d - I₁/d)

F₂/L = (μI/2π) x (I/d - I/d) = 0

The magnitude of the net magnetic force per unit length on the middle bottom is calculated as follows;

F₃/L = (μI₂/2π) x (I₁/d + I₂/d)

F₃/L = (μI/2π) x (I/2d + I/d)

F₃/L = (μI/2π) x (3I/2d)

F₃/L = 3μI²/4πd

Thus, the magnitude of the net magnetic force per unit length on the top wire is μI²/πd.

The magnitude of the net magnetic force per unit length on the middle wire is zero.

The magnitude of the net magnetic force per unit length on the bottom wire is 3μI²/4πd.

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