Question

A solenoid of self-inductance \[1.2{\text{ }}H\] is in series with a tangent galvanometer of reduction factor \[0.9A.\] They are connected to a battery and the tangent galvanometer shows a deflection of \[53^\circ .\] The energy stored in the magnetic field of the solenoid is:
\[\left( {tan{\text{ }}53^\circ {\text{ }} = {\text{ }}\frac{4}{3}} \right)\]
A. $0.864J$
B. $0.72J$
C. $0.173J$
D. $1.44J$

Answer 1

Hint: To solve the question, i.e., to find the energy stored in the magnetic field of the solenoid, we will start with finding the current, because to find the energy we will need the value of current, so after finding the value of current using reduction factor and deflection, we will use the energy formula and get our required answer.

Complete step by step answer:We have been given a solenoid of self-inductance \[1.2{\text{ }}H\] is in series with a tangent galvanometer of reduction factor \[0.9A.\] They are connected to a battery and the tangent galvanometer shows a deflection of \[53^\circ .\] We need to find the energy stored in the magnetic field of the solenoid is:
\[\left( {tan{\text{ }}53^\circ {\text{ }} = {\text{ }}\frac{4}{3}} \right)\]
We know that, current \[ = \] reduction factor \[ \times \] deflection
Here, reduction factor \[ = {\text{ }}0.9,\] deflection \[ = {\text{ }}tan{\text{ }}53^\circ \]
On substituting the value in the above formula, we get
\[\begin{gathered}
   = {\text{ }}0.9{\text{ }} \times {\text{ }}tan53^\circ \\
   = {\text{ }}0.9{\text{ }} \times {\text{ }}\frac{4}{3} \\
   = 1.2{\text{ }}A \\
\end{gathered} \]
Now, to find the energy stored in the magnetic field of the solenoid, we will apply the formula mentioned below.
Energy $ = \frac{{L{i^2}}}{2}$ ​
Here, inductance, (L) \[ = {\text{ }}1.2{\text{ }}H,\] current (i) \[ = {\text{ }}1.2{\text{ }}A\]
On putting the value in the above formula, we get
\[ = \frac{1}{2} \times 1.2 \times {\left( {1.2} \right)^2}\]
\[ = {\text{ }}0.864{\text{ }}J\]
So, the energy stored in the magnetic field of the solenoid is $0.864J.$
Thus, option (A) $0.864J,$ is correct.

Note:In the question, we have been given about solenoid. Let us understand that in detail, so solenoid is a device which is made up of coil of wire used as an electromagnet, it converts electrical energy to mechanical energy. Solenoid creates a magnetic field from electric current and creates linear motion using the magnetic field.