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

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

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

A
Zero
B$\frac{{{\mu _0}}}{{2a}}({i_1} - {i_2})$
C$\frac{{{\mu _0}}}{{2a}}({i_1} + {i_2})$
D$\frac{{{\mu _0}}}{a}({i_1} + {i_2})$(Here ${i_1}$ and ${i_2}$ are the currents flowing in the two parts of the circular conductor of radius $‘a’$ and ${\mu _0}$ has the usual meaning)

Medium

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

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