A uniform wire is bent in the form of a circl | vedclass

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

Question

(A) Let the lengths of the two arcs be $l_1$ (arc $ABC$) and $l_2$ (arc $ADC$). The resistances of these arcs are $R_1 = \rho \frac{l_1}{A_{cross}}$ a

Vedclass · Accepted Answer

Zero

Vedclass · Answer

(A) Let the lengths of the two arcs be $l_1$ (arc $ABC$) and $l_2$ (arc $ADC$). The resistances of these arcs are $R_1 = ho \frac{l_1}{A_{cross}}$ and $R_2 = ho \frac{l_2}{A_{cross}}$.Since the arcs are in parallel,the potential difference across them is the same: $V = I_1 R_1 = I_2 R_2$.This implies $I_1 l_1 = I_2 l_2$,or $\frac{I_1}{I_2} = \frac{l_2}{l_1}$.The magnetic field at the center due to an arc of length $l$ carrying current $i$ is $B = \frac{\mu_0 i 	heta}{4\pi R} = \frac{\mu_0 i l}{4\pi R^2}$.For the two arcs,the magnetic fields are $B_1 = \frac{\mu_0 I_1 l_1}{4\pi R^2}$ and $B_2 = \frac{\mu_0 I_2 l_2}{4\pi R^2}$.Since $I_1 l_1 = I_2 l_2$,we have $B_1 = B_2$.The currents flow in opposite directions around the center,so the magnetic fields produced by the two arcs are in opposite directions.Therefore,the resultant magnetic field at the center is $B_{net} = |B_1 - B_2| = 0$.

$A$ uniform wire is bent in the form of a circle of radius $R$. $A$ current $I$ enters at $A$ and leaves at $C$ as shown in the figure. If the length $ABC$ is half of the length $ADC$,the magnetic field at the centre $O$ will be

Similar Questions

Magnetic field due to a ring having $n$ turns at a distance $x$ on its axis is proportional to (if $r$ = radius of ring)

Consider the magnetic field produced by a long straight current-carrying wire.

$A$ closely packed coil having $1000$ turns has an average radius of $62.8\,cm$. If the current carried by the wire of the coil is $1\,A$,the value of the magnetic field produced at the centre of the coil will be (permeability of free space $\mu_0 = 4\pi \times 10^{-7}\,T\cdot m/A$) nearly:

An arc of a circle of radius $R$ subtends an angle $\frac{\pi}{2}$ at the centre. It carries a current $i$. The magnetic field at the centre will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module