Question

Four identical long solenoids $A$, $B$ and $C$ are connected to each other as shown in the figure. If the magnetic field at the center of $A$ is $3T$, the field at the center of $C$ would be: (Assume that the magnetic field is confined within the volume of the respective solenoid.)

• A. $6T$
• B. $12T$
• C. $1T$
• D. $9T$

Answer 1

The correct option is C

$1T$

Step 1. Given Data,

Magnetic field at center of $B_A=3T$

Step 2. We have to calculate the magnetic field at center of $C,$

Since, the current at $A=I_0$, then it will equally distributed at point $B,$$C$and$D,$

As we know, $B={\mu }_{0}ni$

Where, $B=$magnetic flux density

${\mu }_0=$magnetic constant

$n=$number of turns in the solenoid

$i=$current through the solenoid

Therefore, $B\propto I$

Now,

$\begin{array}{rcl}\frac{B_C}{B_A}& =& \frac{i_C}{i_A}\end{array}$

Where, $B_C=$magnetic field through $C$

$B_A=$magnetic field through $A$

$i_A=$current through $A$

$i_C=$current through $C$

$\Rightarrow$$\begin{array}{rcl}\frac{B_C}{B_A}& =& \frac{{\displaystyle \raisebox{1ex}{$I_0$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}{I_0}\\ & =& \frac{1}{3}\end{array}$

$\Rightarrow$ $\begin{array}{rcl}{B}_C& =& \frac{B_A}{3}\\ & =& \frac{3T}{3}\\ & =& 1T\end{array}$

Hence, the correct option is $\text{'}C\text{'}$.