Question

A one-metre-long wire is lying at right angles to the magnetic field. A force of 1 kg wt is acting on it in a magnetic field of 0.98 Tesla. The current flowing in it will be
A. 100 A
B. 10 A
C. 1 A
D. Zero

Answer 1

Hint: To solve this problem, we have the equation for force acting on a conductor of length l carrying a current I and placing it in a magnetic field of magnitude B. Also, we know that SI unit of force is newton. After converting the given value to SI unit, we can find the current flowing through the conductor.

Formula used:
The force on a current carrying conductor is,
$F=Bil\sin \theta $
where i is the current flowing through the circuit and ϴ is the angle between the wire and magnetic field.

Complete step by step solution:
We know that magnetic fields are produced due to current carrying in a conductor. The magnetic field produced will exert a force on the conductor. We have the direct equation for the force acting on the current carrying conductor of length l and magnetic field B as: force acting on conductor,
$F=i(l\times B)$
That is,
$F=Bil\sin \theta $

From this equation we can say that when current increases, the force also increases. But in the question, the length of wire and magnetic field are at right angles to each other. That is,
sinϴ=sin 90=1
As magnitude sin is 1, we can ignore that term.
Therefore, force acting on the conductor, F=Bil

In this question, force acting on the conductor= 1 kg wt= 9.8N
Length of the conductor = 1 m
Magnetic field= 0.98 T
On substituting, we get
The current flowing in the circuit,
$i=\dfrac{F}{Bl}=\dfrac{9.8}{0.98\times 1}=10\,A$

Therefore, the answer is option B.

Note: Don’t forget to convert force to SI unit. For converting kgwt to SI unit Newton, we have to multiply kgwt with acceleration due to gravity. That is, we have to multiply kgwt with 9.8m/s. a magnetic field produced by a current carrying conductor will also exert a force on the magnet.