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# 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 intensity of the magnetic field at the centre due to a constant current in the ring is

$\begin {array} {1 1} (a)\;Proportional\: to (180^{\circ}- \theta) & \quad (b)\;Inversely\: proportional\: to\: r \\ (c)\;Zero\: only\: if\: \theta = 180^{\circ} & \quad (d)\;Zero\: for \: all\: values\: of\: \theta \end {array}$

Can you answer this question?

Field at the centre due to the two parts is in the opposite direction and is proportional
to current in each arcs and to the angle subtended at the centre
Current is inversely proportional to resistance => it is inversely proportional to length (angle)
$\therefore$ Current times the angle is constant
Ans : (d)
answered Feb 23, 2014