Assertion : The magnetic field at the centre | vedclass

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

Question

(D) The magnetic field at the center of a circular arc of radius $R$ carrying current $I$ and subtending an angle $\phi$ at the center is given by $B

Vedclass · Accepted Answer

If both the Assertion and Reason are incorrect.

Vedclass · Answer

(D) The magnetic field at the center of a circular arc of radius $R$ carrying current $I$ and subtending an angle $\phi$ at the center is given by $B = \frac{\phi}{2\pi} \cdot \frac{\mu_0 I}{2R}$.For the given coil,the current $I$ splits into $I_1$ and $I_2$ along arcs subtending angles $	heta$ and $(2\pi - 	heta)$ respectively.The magnetic field due to arc $I_1$ is $B_1 = \frac{	heta}{2\pi} \cdot \frac{\mu_0 I_1}{2R}$ (directed into the page).The magnetic field due to arc $I_2$ is $B_2 = \frac{2\pi - 	heta}{2\pi} \cdot \frac{\mu_0 I_2}{2R}$ (directed out of the page).For the net magnetic field to be zero,$B_1 = B_2$,which implies $	heta I_1 = (2\pi - 	heta) I_2$.This condition is not satisfied simply by $I_1 = I_2$ unless $	heta = \pi$ (i.e.,the currents split into two semicircles). Therefore,the Assertion is generally false,and the Reason is also incorrect as $I_1 = I_2$ does not guarantee zero field unless the geometry is symmetric.

Assertion : The magnetic field at the centre of the circular coil in the following figure due to the currents $I_1$ and $I_2$ is zero.
Reason : $I_1 = I_2$ implies that the fields due to the current $I_1$ and $I_2$ will be balanced.

Similar Questions

The magnetic field $d\overrightarrow{B}$ due to a small current element $d\overrightarrow{l}$ at a distance $\overrightarrow{r}$ from an element carrying current $i$ is given by:

$A$ long straight wire of circular cross-section is made of a non-magnetic material. The wire is of radius $a$. The wire carries a current $I$ which is uniformly distributed over its cross-section. The energy stored per unit length in the magnetic field contained within the wire is

Derive an expression for the force per unit length between two infinitely long straight parallel current-carrying wires. Hence,define one ampere $(A)$.

In a hydrogen atom,an electron moves in a circular orbit of radius $5.2 \times 10^{-11} \, m$ and produces a magnetic induction of $12.56 \, T$ at its nucleus. The current produced by the motion of the electron will be (Given $\mu_0 = 4\pi \times 10^{-7} \, Wb/A \cdot m$)

Two infinitely long parallel wires carry equal current in the same direction. The magnetic field at a midpoint between the two wires is

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Assertion : The magnetic field at the centre of the circular coil in the following figure due to the currents $I_1$ and $I_2$ is zero.Reason : $I_1 = I_2$ implies that the fields due to the current $I_1$ and $I_2$ will be balanced.