A toroid is a long coil of wire (N turns) wou | vedclass

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

Question

(D) The coefficient of self-induction $L$ is defined as $L = \frac{\phi}{I}$,where $\phi$ is the total magnetic flux linked with the coil and $I$ is t

Vedclass · Accepted Answer

$\frac{\mu_0 N^2 r^2}{2 R}$

Vedclass · Answer

(D) The coefficient of self-induction $L$ is defined as $L = \frac{\phi}{I}$,where $\phi$ is the total magnetic flux linked with the coil and $I$ is the current flowing through it.For a toroid with $N$ turns,the total flux $\phi$ is given by $\phi = N \cdot A \cdot B$,where $A$ is the cross-sectional area of the toroid and $B$ is the magnetic field inside it.The cross-sectional area $A = \pi r^2$.The magnetic field inside a toroid is $B = \mu_0 n I$,where $n = \frac{N}{2 \pi R}$ is the number of turns per unit length.Substituting these into the flux equation:$\phi = N (\pi r^2) (\mu_0 \frac{N}{2 \pi R} I) = \frac{\mu_0 N^2 r^2 I}{2 R}$.Finally,the self-induction $L = \frac{\phi}{I} = \frac{\mu_0 N^2 r^2}{2 R}$.

$A$ toroid is a long coil of wire ($N$ turns) wound over a circular core. The coefficient of self-induction of the toroid is [The magnetic field in it is uniform and $R >> r$,where $r=$ radius of wire,$R=$ radius of coil] ($\mu_0=$ permeability of free space).

Similar Questions

$A$ graph of magnetic flux $(\phi)$ versus current $(I)$ is plotted for four inductors $A, B, C, D$. Which inductor has the largest value of self-inductance?

Select the incorrect unit of self inductance.

The self-inductance of an air-cored solenoid of length $40 \ cm$,diameter $7 \ cm$ having $200$ turns is nearly: (in $\mu H$)

Current in a circuit falls from $5.0\, A$ to $0\, A$ in $0.1\, s$. If an average $emf$ of $200\, V$ is induced,estimate the self-inductance of the circuit in $H$.

When current $I$ passes through an inductor having self-inductance of $4 \ H$. If the current is made double,what will be the new self-inductance of the inductor?

Vedclass Test Series

Exam Paper Generator

Online Exam Module