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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(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).

Similar Questions

$A$ circular coil of wire consisting of $100$ turns,each of radius $8.0 \; cm$,carries a current of $0.40 \; A$. What is the magnitude of the magnetic field $B$ at the centre of the coil?

Two infinite length wires carry currents $8 \ A$ and $6 \ A$ respectively and are placed along the $X$ and $Y$ axes respectively. The magnetic field at a point $P(0, 0, d)$ will be:

Current through $ABC$ and $A^{\prime} B^{\prime} C^{\prime}$ is $I$. What is the magnetic field at $P$? $BP = PB^{\prime} = r$. (Here $C^{\prime} B^{\prime} PBC$ are collinear).

Find the resultant magnetic field at the origin due to four infinitely long wires. Each wire produces a magnetic field of magnitude $B$ at the origin.

Vedclass Test Series

Exam Paper Generator

Online Exam Module