Two very long, straight, parallel conductors A and B carry current of 5 A and 10 A respectively and are at a d

Question

Two very long, straight, parallel conductors A and B carry current of 5 A and 10 A respectively and are at a distance of 10 cm from each other. The direction of the current in the two conductors is the same. The force acting per unit length between two conductors is: ($\mu_0=4\pi 	imes 10^{-7}$ SI unit)

Accepted Answer

1.  **Identify Formula:** The magnetic force per unit length ($F/l$) between two infinite parallel current-carrying conductors is given by:
    $$\frac{F}{l} = \frac{\mu_0 I_1 I_2}{2\pi d}$$
    where $I_1$ and $I_2$ are the currents and $d$ is the separation distance.
2.  **Substitute Values:**
    *   $I_1 = 5 	ext{ A}$
    *   $I_2 = 10 	ext{ A}$
    *   $d = 10 	ext{ cm} = 0.1 	ext{ m}$
    *   $\mu_0 = 4\pi 	imes 10^{-7} 	ext{ T m/A}$
    $$\frac{F}{l} = \frac{(4\pi 	imes 10^{-7}) 	imes 5 	imes 10}{2\pi 	imes 0.1}$$
3.  **Calculate Magnitude:**
    $$\frac{F}{l} = \frac{2 	imes 10^{-7} 	imes 50}{0.1} = \frac{100 	imes 10^{-7}}{0.1} = \frac{10^{-5}}{10^{-1}} = 10^{-4} 	ext{ N m}^{-1}$$
4.  **Determine Direction:**
    *   Currents flowing in the **same direction** attract each other.
    *   Currents flowing in **opposite directions** repel each other.
    *   Since the problem states the direction is the same, the force is **attractive**.
5.  **Conclusion:** The force is $1 	imes 10^{-4} 	ext{ N m}^{-1}$ and is attractive.

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