Question

A thin straight strip of length \[5cm\] and magnetic moment \[0.5A{m^2}\] was bent such that there is a gap of \[1cm\] at its end. Then the magnetic moment will be (nearly):
A) \[0.1A{m^2}\]
B) \[0.2A{m^2}\]
C) \[0.05A{m^2}\]
D) \[0.25A{m^2}\]

Answer 1

Hint: Since the same strip is bent, current flowing through the strip and after the strip is bent, is the same. Using the formula of magnetic moment and considering the current flowing to be constant, the required magnetic moment can be obtained.

Complete step by step answer:
Magnetic Moment through a current loop is:
(I) directly proportional to the current flowing through the loop
(ii) Directly proportional to the area of cross-section (A) of the loop.
The formula for Magnetic Moment can be formulated as:
\[\vec M = I\vec A\]
\[\vec M = \]Magnetic Moment
\[I = \]Current through the loop
\[\vec A = \] Area of the loop
Let us consider the following:
\[{L_1} = \] Length of the strip
\[{L_2} = \] Length of the ends
 \[{M_1} = \] Magnetic moment of the strip
\[{M_2} = \] Required magnetic moment.
Since the current flowing through the coils is constant:
\[\dfrac{{{M_1}}}{{{L_1}}} = \dfrac{{{M_2}}}{{{L_2}}}\]
Putting the given values:
\[\dfrac{{0.5}}{5} = \dfrac{{{M_2}}}{1}\]
Thus we obtain:
\[{M_2} = 0.1A{m^2}\]
This is our required solution.

Option (A) is correct.

Note: Both \[\vec M\] and \[\vec A\] are vector quantities having both magnitude and direction. The direction of \[\vec A\] and as a result \[\vec M\] is perpendicular to the plane of the coil. The direction of \[\vec M\] and \[\vec A\] can be obtained using the right hand thumb rule. The fingers curl such that it represents the direction of current and the thumb points to the direction of magnetic moment and area vector.