Four identical long solenoids A, B, C and D a | vedclass

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(D) The magnetic field $B$ at the center of a long solenoid is given by $B = \mu_0 n i$,where $n$ is the number of turns per unit length and $i$ is th

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(D) The magnetic field $B$ at the center of a long solenoid is given by $B = \mu_0 n i$,where $n$ is the number of turns per unit length and $i$ is the current flowing through it.Since the solenoids are identical,$n$ is the same for all.Thus,$B \propto i$.Let the total current entering the circuit be $I$. This current $I$ flows through solenoid $A$.At the junction,the current $I$ splits into three identical parallel branches containing solenoids $B, C,$ and $D$.Since the solenoids are identical,their resistances are equal,and the current $I$ divides equally among the three branches.Therefore,the current through solenoid $C$ is $i_C = \frac{I}{3}$.Given that the magnetic field at the center of $A$ is $B_A = 3\, T$,we have $B_A \propto I$,so $3\, T \propto I$.The magnetic field at the center of $C$ is $B_C \propto i_C = \frac{I}{3}$.Therefore,$B_C = \frac{B_A}{3} = \frac{3\, T}{3} = 1\, T$.

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

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