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A current $i$ ampere flows in a circular arc of wire whose radius is $R$, which subtend an angle $3\pi /2$ radian at its centre. The magnetic induction at the centre is
An electron enters the space between the plates of a charged capacitor as shown. The charge density on the plate is $\sigma $. Electric intensity in the space between the plates is $E$. A uniform magnetic field $B$ also exists in that space perpendicular to the direction of $E$. The electron moves perpendicular to both $\vec E$ and $\vec B$ without any change in direction. The time taken by the electron to travel a distance $\ell $ is the space is
An ammeter and a voltmeter of resistance $R$ are connected in series to an electric cell of negligible internal resistance. Their readings are $A$ and $V$ respectively. If another resistance $R$ is connected in parallel with the voltmeter
The current in flowing along the path $A B C D$ of a cube (shown in the left figure) produces a magnetic field at the centre of cube of magnitude $B$. Dashed line depicts the non-conducting part of the cube. Consider a cubical shape shown to the right which is identical in size and shape to the left. If the same current now flows in along the path $D A E F G C D$, then the magnitude of magnetic field at the centre will be
Two very long, straight and insulated wires are kept at $90^o$ angle from each other In $xy -$ plane as shown in the figure. These wires carry current of equal magnitude $I$, whose directions are shown in the figure. The net magnetic field at point $P$ will be
The figure shows three situations when an electron moves with velocity $\vec v$ travels through a uniform magnetic field $\vec B$. In each case, what is the direction of magnetic force on the electron
A horizontal overhead power line is at a height of $4\,m$ from the ground and carries a current of $100\,A$ from east to west. The magnetic field directly below it on the ground is $(\mu _0 = 4\pi \times 10^{-7}\,TmA^{-1})$
The current flowing in a coil of resistance $90 \,\Omega$ is to be reduced by $90\%$. What value of resistance should be connected in parallel with it ............. $\Omega $
As shown in the figure, the uniform magnetic field between the two identical plates is $B$. There is a hole in plate. If through this hole a particle of charge $q$, mass $m$ and energy $E$ enters this magnetic field, then the particle will not collide with the upper plate provided