Search any question & find its solution
Question:
Answered & Verified by Expert
$A$ and $B$ are two infinitely long straight parallel conductors. $C$ is another straight conductor of length $1 \mathrm{~m}$ kept parallel to $A$ and $B$ as shown in the figure. Then the force experienced by $C$ is
Options:
Solution:
1908 Upvotes
Verified Answer
The correct answer is:
towards $B$ equal to $06 . \times 10^{-5} \mathrm{~N}$
The force between the conductors is attractive if the currents in them are in the same direction and repulsive if the currents are in opposite direction Mutual force between conductors $A$ and $C$
$$
\begin{aligned}
F_{1} &=\frac{\mu_{0}}{2 \pi} \frac{I_{1} I_{2} l}{r} \\
&=\frac{\mu_{0}}{2 \pi} \frac{2 \times 3 \times 1}{0.05} \\
&=2.40 \times 10^{-5} \mathrm{~N} \text { (towards } A \text { ) }
\end{aligned}
$$
Mutual force between conductors $B$ and $C$
$$
\begin{aligned}
&=\frac{\mu_{0}}{2 \pi} \times \frac{4 \times 3 \times 1}{0.08} \\
&=3 \times 10^{-5} \mathrm{~N} \text { (towards } B \text { ) }
\end{aligned}
$$
Hence, the resultant force experienced by $C$
$$
\begin{aligned}
&=(3-2.4) \times 10^{-5} \mathrm{~N} \\
&=0.6 \times 10^{-5} \mathrm{~N}(\text { towards } B)
\end{aligned}
$$
$$
\begin{aligned}
F_{1} &=\frac{\mu_{0}}{2 \pi} \frac{I_{1} I_{2} l}{r} \\
&=\frac{\mu_{0}}{2 \pi} \frac{2 \times 3 \times 1}{0.05} \\
&=2.40 \times 10^{-5} \mathrm{~N} \text { (towards } A \text { ) }
\end{aligned}
$$
Mutual force between conductors $B$ and $C$
$$
\begin{aligned}
&=\frac{\mu_{0}}{2 \pi} \times \frac{4 \times 3 \times 1}{0.08} \\
&=3 \times 10^{-5} \mathrm{~N} \text { (towards } B \text { ) }
\end{aligned}
$$
Hence, the resultant force experienced by $C$
$$
\begin{aligned}
&=(3-2.4) \times 10^{-5} \mathrm{~N} \\
&=0.6 \times 10^{-5} \mathrm{~N}(\text { towards } B)
\end{aligned}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.