A closely packed coil having $1000$ turns has an average radius of $62.8\,cm$. If current carried by the wire of the coil is $1\,A$, the value of magnetic field produced at the centre of the coil will be (permeability of free space $=4 \pi \times 10^{-7}\,H / m$ ) nearly
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A voltmeter has a range $0-V$ with a series resistance $R$. With a series resistance $2R$, the range is $0-V'$. The correct relation between $V$ and $V'$ is
An element $d l=d x \hat{l}$ (where, $d x=1\, cm$ ) is placed at the origin and carries a large current $i=10 A$. What is the magnetic field on the $Y$ -axis at a distance of $0.5\, m$ ?
The resistance of a galvanometer is $25\, ohm$ and it requires $50\,\mu A$ for full deflection. The value of the shunt resistance required to convert it into an ammeter of $5\, amp$ is
A current $I$ flows in an infinitely long wire with cross-section in the form of a semicircular ring of radius $R$ . The magnitude of the magnetic induction along its axis is
Two resistances $R_1=X \Omega$ and $R_2=1 \Omega$ are connected to a wire $A B$ of uniform resistivity, as shown in the figure. The radius of the wire varies linearly along its axis from $0.2 mm$ at $A$ to $1 mm$ at $B$. A galvanometer ($G$) connected to the center of the wire, $50 cm$ from each end along its axis, shows zero deflection when $A$ and $B$ are connected to a battery. The value of $X$ is. . . . .