Question

A uniform conducting wire $ABC$ lying in a $XY$ plane has a mass of $10g$ . A current of $2A$ flows through it. The wire is kept in a uniform magnetic field $B = 2T$ which acceleration of the wire is:
A. Zero
B. $12m{\text{ }}{s^{ - 2}}$ and along the positive Y-axis.
C. $1.2 \times {10^{ - 3}}m{\text{ }}{s^{ - 2}}$ along the positive Y-axis.
D. $0.6m{\text{ }}{s^{ - 2}}$ along the positive X-axis.

Answer 1

Hint: In this type of question, first we will find the force due to the magnetic field and then substituting on the formula given by Newton's law we will find the acceleration of the wire. As the magnitude of the field produced will be the same, we can find the answer directly.

Formula used:
\[f = Bl\sin \theta \]
Where,
$f$ is the force,
$B$ is the magnetic field,
$l$ is the length and
$i$ is the current.

Complete step by step answer:

According to the question, it is given that
Mass, $m = 10g$
Current, $i = 2A$
Magnetic field, $B = 2T$
$\theta = {90^ \circ }$
And from the figure, $AC = 3$
Now, let the force given on $AC$ is $f$
And we know that,
$f = Bl\sin \theta $
Now, substituting the value in above equation,
\[
  f = Bil\sin \theta \\
   \Rightarrow f = 2 \times 2 \times 3 \times {10^{ - 2}} \times \sin {90^ \circ } \\
 \]
\[ \Rightarrow f = 12 \times {10^{ - 2}}N\] (Along Y-axis)
Now we will calculate the acceleration, and we know that
$
  F = ma \\
   \Rightarrow a = \dfrac{F}{m} \\
 $
Now, substituting the value in above equation,
$ \Rightarrow a = \dfrac{{12 \times {{10}^{ - 2}}N}}{{10 \times {{10}^{ - 3}}}}$
$ \Rightarrow a = 12m{\text{ }}{s^{ - 2}}$ (Along Y-axis)
So, the acceleration is $12m{\text{ }}{s^{ - 2}}$ along positive Y-axis
Hence, the correct option is B.

Note:
Take care of units as if you don’t convert the unit in standard format, you can make mistakes and remember that,
$F = Bil\sin \theta $, where. F is force acting on a current carrying conductor is magnetic flux density (magnetic field strength), i is magnitude of current flowing through the conductor, l is length of conductor, θ is angle that conductor makes with the magnetic field.