Question 19: Magnetism and Matter

Question

Three long straight wires carrying current are arranged mutually parallel as shown in the figure. The force experienced by 15 cm length of wire $Q$ is $\_\_\_\_$ .
$$ \left(\mu_{\mathrm{o}}=4 \pi 	imes 10^{-7} \mathrm{~T} . \mathrm{m} / \mathrm{A}ight) $$

Accepted Answer

Using the formula for the force per unit length between two parallel current-carrying wires :
$$ \frac{F}{l}=\frac{\mu_0 I_1 I_2}{2 \pi r} $$
Wires P and Q carry currents in opposite directions (3 A up and 1 A down). Parallel wires with opposite currents repel each other. Therefore, wire $P$ pushes wire $Q$ to the right (towards wire $R$ ) with a force $F_{P Q}$
Given $\mathrm{I}_{\mathrm{P}}=3 \mathrm{~A}, \mathrm{I}_{\mathrm{Q}}=1 \mathrm{~A}, \mathrm{r}_{\mathrm{PQ}}=3 \mathrm{~cm}=0.03 \mathrm{~m}$
So, the magnitude of force on 15 cm of wire Q due to wire P is,
$$ \mathrm{F}_{\mathrm{PQ}}=\frac{\left(4 \pi 	imes 10^{-7}ight) 	imes 3 	imes 1 	imes 0.15}{2 \pi 	imes 0.03} \mathrm{~N}=3 	imes 10^{-6} \mathrm{~N} $$
Wires Q and R carry currents in the same direction ( 1 A down and 2 A down). Parallel wires with samedirection currents attract each other. Therefore, wire $R$ pulls wire $Q$ to the right (towards wire $R$ ) with force $F_{R Q}$.
Given that $\mathrm{I}_{\mathrm{R}}=2 \mathrm{~A}, \mathrm{I}_{\mathrm{Q}}=1 \mathrm{~A}, \mathrm{r}_{\mathrm{RQ}}=2 \mathrm{~cm}=0.02 \mathrm{~m}$
$$ \mathrm{F}_{\mathrm{RQ}}=\frac{\left(4 \pi 	imes 10^{-7}ight) 	imes 2 	imes 1 	imes 0.15}{2 \pi 	imes 0.02} $$
$$\Rightarrow $$ $$ \mathrm{F}_{\mathrm{RQ}}=\frac{2 	imes 10^{-7} 	imes 0.30}{0.02}=2 	imes 10^{-7} 	imes 15=3 	imes 10^{-6} \mathrm{~N} $$
Since both forces acting on wire $Q$ are directed towards the right, the net force will be towards $R$.
$$ \mathrm{F}_{\mathrm{net}}=\mathrm{F}_{\mathrm{PQ}}+\mathrm{F}_{\mathrm{RQ}} $$
$$\Rightarrow $$ $\mathrm{F}_{	ext {net }}=3 	imes 10^{-6}+3 	imes 10^{-6}$
$$ F_{n e t}=6 	imes 10^{-6} \mathrm{~N} $$
Hence, the net force acting on wire $Q$ is $6 	imes 10^{-6} \mathrm{~N}$ towards $R$.
Hence, the correct option is (B).

Answer

$6 	imes 10^{-6} \mathrm{~N}$ towards $P$

Answer

$6 	imes 10^{-6} \mathrm{~N}$ towards $R$

Answer

$6 	imes 10^{-7} \mathrm{~N}$ towards $P$

Answer

$6 	imes 10^{-7} \mathrm{~N}$ towards $R$

Magnetism and Matter

Three long straight wires carrying current are arranged mutually parallel as shown in the figure. The force experienced by 15 cm length of wire Q is \_\_\_\_ . $ \left(\mu_{\mathrm{o}}=4 \pi \times 10^{-7} \mathrm{~T} . \mathrm{m} / \mathrm{A}\right)

Choose the correct answer: