A cell is connected between two points of a u | vedclass

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

Question

(A) The magnetic field at the center of a circular arc of radius $r$ carrying current $i$ is given by $B = \frac{\mu_0 i 	heta}{4\pi r}$.Since the tw

Vedclass · Accepted Answer

Zero

Vedclass · Answer

(A) The magnetic field at the center of a circular arc of radius $r$ carrying current $i$ is given by $B = \frac{\mu_0 i 	heta}{4\pi r}$.Since the two parts of the circular conductor are connected in parallel to the cell,the potential difference $V$ across them is the same.Let $R_1$ and $R_2$ be the resistances of the two parts with lengths $l_1$ and $l_2$ respectively. Then $V = i_1 R_1 = i_2 R_2$.Since $R = ho \frac{l}{A}$,we have $i_1 ho \frac{l_1}{A} = i_2 ho \frac{l_2}{A}$,which implies $i_1 l_1 = i_2 l_2$.The magnetic field due to the first part is $B_1 = \frac{\mu_0 i_1 	heta_1}{4\pi r}$ and due to the second part is $B_2 = \frac{\mu_0 i_2 	heta_2}{4\pi r}$.Since $l_1 = r 	heta_1$ and $l_2 = r 	heta_2$,we have $i_1 r 	heta_1 = i_2 r 	heta_2$,so $i_1 	heta_1 = i_2 	heta_2$.Thus,$B_1 = \frac{\mu_0}{4\pi r} (i_1 	heta_1)$ and $B_2 = \frac{\mu_0}{4\pi r} (i_2 	heta_2)$.Since $i_1 	heta_1 = i_2 	heta_2$,the magnitudes are equal $(B_1 = B_2)$.Because the currents flow in opposite directions around the center,the magnetic fields produced by the two parts are equal in magnitude and opposite in direction.Therefore,the resultant magnetic field at the center is zero.

$A$ cell is connected between two points of a uniformly thick circular conductor. The magnetic field at the centre of the loop will be

Similar Questions

$A$ wire in the form of a circular loop of one turn carrying a current produces a magnetic field $B$ at the centre. If the same wire is looped into a coil of two turns and carries the same current,the new value of magnetic induction at the centre is

$A$ circular coil of wire consisting of $100$ turns,each of radius $8.0 \; cm$,carries a current of $0.40 \; A$. What is the magnitude of the magnetic field $B$ at the centre of the coil?

Two similar coils each of radius $R$ are lying concentrically with their planes at right angles to each other. The currents flowing in them are $I$ and $2I$. The resultant magnetic field of induction at the centre will be ($\mu_0 =$ Permeability of vacuum).

Which of the following graphs represents the magnetic field $(B)$ versus distance $(r)$ from the centre of a long straight conducting wire of uniform cross-sectional area carrying a steady current $I$ and having radius $a$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module