A toroid has a core of inner radius r_1 and o | vedclass

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

Question

(B) To find the magnetic field inside the toroid,we use Ampere's Circuital Law.Consider an Amperian loop of radius $r$ inside the toroid,where $r = \f

Vedclass · Accepted Answer

$\frac{\mu_0 N I}{\pi(r_1+r_2)}$

Vedclass · Answer

(B) To find the magnetic field inside the toroid,we use Ampere's Circuital Law.Consider an Amperian loop of radius $r$ inside the toroid,where $r = \frac{r_1 + r_2}{2}$.According to Ampere's Law: $\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{	ext{enclosed}}$.Since the magnetic field $B$ is uniform along the circular path and parallel to the length element $d\vec{l}$,the angle between them is $0^\circ$.Thus,$B \oint dl = \mu_0 N I$.The circumference of the loop is $2 \pi r = 2 \pi \left( \frac{r_1 + r_2}{2} ight) = \pi(r_1 + r_2)$.Substituting this into the equation: $B \cdot \pi(r_1 + r_2) = \mu_0 N I$.Therefore,the magnetic field is $B = \frac{\mu_0 N I}{\pi(r_1 + r_2)}$.

$A$ toroid has a core of inner radius $r_1$ and outer radius $r_2$,around which $N$ turns of wire are wound. If the current in the wire is $I$,then the magnetic field inside the toroid is $(\mu_0 = \text{permeability of free space})$

Similar Questions

$A$ long solenoid is formed by winding $70$ turns $cm^{-1}$. If $2.0\,A$ current flows,then the magnetic field produced inside the solenoid is $.......\times 10^{-4}\,T$ $\left(\mu_0 = 4\pi \times 10^{-7}\,TmA^{-1}\right)$

The magnetic field $B$ within a solenoid having $n$ turns per meter length and carrying a current of $i$ amperes is given by:

From Ampere's circuital law for a long straight wire of circular cross-section carrying a steady current,the variation of magnetic field in the inside and outside region of the wire is :

The current required to be passed through a solenoid of $15\,cm$ length and $60$ turns in order to demagnetize a bar magnet of magnetic intensity $2.4 \times 10^3\,A/m$ is $.........A$.

The magnetic field at the centre of a long solenoid having $400$ turns per unit length and carrying a current $i$ is $6.24 \times 10^{-2} \,T$. The magnetic field at the centre of another long solenoid having $200$ turns per unit length and carrying a current $\frac{i}{2}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module