A battery is connected between two points A and B on the circumference of a uniform conducting ring of radius r and resistance R. One

Q: A battery is connected between two points $A$ and $B$ on the circumference of a uniform conducting ring of radius $r$ and resistance $R$. One of the arcs $AB$ of the ring subtends an angle $\theta $ at the centre. The value of the magnetic induction at the centre due to the current in the ring is

d (d) Directions of currents in two parts are different, so directions of magnetic fields due to these currents are opposite. Also applying Ohm’s law across $AB$ ${i_1}{R_1} = {i_2}{R_2} \Rightarrow {i_1}{l_2} = {i_2}{l_2}$ $\left( {\;R = \rho \frac{l}{A}} \right)$ Also ${B_1} = \frac{{{\mu _o}}}{{4\pi }} \times \frac{{{i_1}{l_1}}}{{{r^2}}}$ and ${B_2} = \frac{{{\mu _o}}}{{4\pi }} \times \frac{{{i_2}{l_2}}}{{{r^2}}}$ ($\;l = r\theta $) $\therefore \,\frac{{{B_2}}}{{{B_1}}} = \frac{{{i_1}{l_1}}}{{{i_2}{l_2}}} = 1$ Hence, two field induction’s are equal but of opposite direction. So, resultant magnetic induction at the centre is zero and is independent of $\theta $.

SECTION - A [PHYSICS - MCQ]

GSEB - English Medium

A battery is connected between two points $A$ and $B$ on the circumference of a uniform conducting ring of radius $r$ and resistance $R$. One of the arcs $AB$ of the ring subtends an angle $\theta $ at the centre. The value of the magnetic induction at the centre due to the current in the ring is

AProportional to $2\,(180^\circ - \theta )$
BInversely proportional to $r$
CZero, only if $\theta = 180^\circ $
DZero for all values of $\theta $

IIT 1995, Medium

STD 11 Science
NEET
STD 12 - 4. Moving charges and magnetism
Physics

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