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Two long, parallel wires carry currents $I_1$ and $I_2$ in the **same direction** separated by distance $d$. The force per unit length between them is:
ARepulsive, $\dfrac{\mu_0 I_1 I_2}{2\pi d}$
BAttractive, $\dfrac{\mu_0 I_1 I_2}{2\pi d}$
CZero
DAttractive, $\dfrac{\mu_0 I_1 I_2}{4\pi d^2}$
Answer & Solution
Correct answer: B. Attractive, $\dfrac{\mu_0 I_1 I_2}{2\pi d}$
Each wire sits in the magnetic field of the other. The field of wire 1 at the position of wire 2 has magnitude $B_1 = \dfrac{\mu_0 I_1}{2\pi d}$.
Force per unit length on wire 2: $\dfrac{F}{L} = I_2 B_1 = \dfrac{\mu_0 I_1 I_2}{2\pi d}$.
**Direction**: when currents flow in the *same* direction, the force is **attractive**; in *opposite* directions, the force is **repulsive**. This is also how the ampere is operationally defined (the current that, in two parallel wires 1 m apart, produces $2 \times 10^{-7}$ N per metre).
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