A wire bent in the shape of a regular n-polyg | vedclass

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

Question

(A) For an $n$-sided polygon,the magnetic field due to one side at the centre of the loop using the Biot-Savart law is given by:$B_1 = \frac{\mu_0 I}{

Vedclass · Accepted Answer

$\frac{n \mu_0 I}{2 \pi l} \sin (\pi / n)$

Vedclass · Answer

(A) For an $n$-sided polygon,the magnetic field due to one side at the centre of the loop using the Biot-Savart law is given by:$B_1 = \frac{\mu_0 I}{4 \pi l} (\sin 	heta_1 + \sin 	heta_2)$As there are $n$ sides,the angle subtended by one side at the centre is $\alpha = \frac{2 \pi}{n}$.Therefore,$	heta_1 = 	heta_2 = \frac{1}{2} 	imes \frac{2 \pi}{n} = \frac{\pi}{n}$.Substituting this into the expression for $B_1$:$B_1 = \frac{\mu_0 I}{4 \pi l} (\sin \frac{\pi}{n} + \sin \frac{\pi}{n}) = \frac{\mu_0 I}{2 \pi l} \sin \frac{\pi}{n}$.The magnetic field at the centre due to all $n$ segments is the sum of the fields due to each segment:$B = n 	imes B_1 = \frac{n \mu_0 I}{2 \pi l} \sin \left(\frac{\pi}{n}ight)$.

$A$ wire bent in the shape of a regular $n$-polygonal loop carries a steady current $I$. Let $l$ be the perpendicular distance of a given segment and $R$ be the distance of a vertex from the centre of the loop. The magnitude of the magnetic field at the centre of the loop is given by

Similar Questions

$A$ horizontal overhead power line is at a height of $4\, m$ from the ground and carries a current of $100\, A$ from west to east. The magnetic field directly below it on the ground is $(\mu_0 = 4\pi \times 10^{-7}\, T\, m A^{-1})$.

$A$ coil of $50$ turns and $4$ cm radius carries $2$ $A$ current. The magnetic field at its centre is ....... $mT$.

Two long parallel wires are at a distance $2d$ apart. They carry steady equal currents flowing out of the plane of the paper,as shown. The variation of the magnetic field $B$ along the line $XX'$ is given by

If we double the radius of a coil keeping the current through it unchanged,then the magnetic field at any point at a large distance from the centre becomes approximately

If the strength of the magnetic field produced $10\,cm$ away from an infinitely long straight conductor is ${10^{ - 5}}\,Wb/m^2$,the value of the current flowing in the conductor will be........$A$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module