Question

A bar magnet of magnetic moment \[3.0\,A - {m^2}\] is placed in a uniform magnetic induction field of \[2 \times {10^{ - 5}}T\]. If each pole of the magnetic experiences a force of \[6 \times {10^{ - 4}}N\], the length of the magnet is:
A. \[0.5\,m\]
B. \[0.3\,m\]
C. \[0.2\,m\]
D. \[0.1\,m\]

Answer 1

Hint: Use the Formula of Magnetic Moment and substitute the values in formula as given in the Question to get the answer. The magnetic moment is a vector relating torque of an object to the magnetic field. This is mathematically represented as:
\[\tau = m \times B\]
Where,
τ is the torque acting on the dipole
m is magnetic moment
and B is the external magnetic field

Complete step by step answer:
Magnetic Moment- The magnetic moment can be defined as the magnetic strength and orientation of a magnet or other object that creates a magnetic field. Permanent magnets, Astronomical objects, Loops of electric current, Elementary particles are some examples of the objects having magnetic moments.
We know that,
\[M = mL\]
\[m = \dfrac{M}{L}\]
Now, we have
\[F = mB\]
\[F = \dfrac{M}{L}B\]
The above equation can be also written as
\[L = \dfrac{{MB}}{F}\]
On Substituting the values magnetic moment (M) and uniform magnetic field (B), and magnetic experiences of force (F) we will get
\[L = \dfrac{{3 \times 2 \times {{10}^{ - 5}}}}{{6 \times {{10}^{ - 4}}}}\]
After solving the equation we will get,
\[L = 0.1m\]
Thus, the correct answer will be option D i.e, \[L = 0.1\,m\]

So, the correct answer is “Option D”.

Note:
The term magnetic moment usually represents the system's magnetic dipole moment.
And the component of the magnetic moment is represented by an equivalent magnetic dipole which is divided into a magnetic north and South Pole by a very minor distance.