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A cell is connected between the points $A$ and $C$ of a circular conductor $ABCD$ of centre $O$ with angle $AOC = {60^o}$. If ${B_1}$ and ${B_2}$ are the magnitudes of the magnetic fields at $O$ due to the currents in $ABC$ and $ADC$ respectively, the ratio $\frac{{{B_1}}}{{{B_2}}}$ is
An electron is projected with velocity $\vec v$ in a uniform magnetic field $\vec B$ . The angle $\theta$ between $\vec v$ and $\vec B$ lines between $0^o$ and $\frac{\pi}{2}$ . It velocity $\vec v$ vector returns to its initial value in time interval of
A voltmeter has a resistance of $G\, ohms$ and range $V\, volts$. The value of resistance used in series to convert it into a voltmeter of range $nV$ $volts$ is
A very long straight wire carries a current $I$. At the instant when a charge $ + Q$ at point $P$ has velocity $\overrightarrow V $, as shown, the force on the charge is
An electron enters a chamber in which a uniform magnetic field is present as shown below. An electric field of appropriate magnitude is also applied, so that the electron travels undeviated without any change in its speed through the chamber. We are ignoring gravity. Then, the direction of the electric field is
Two straight infinitely long current carrying wires are kept along $z-$ axis at the coordinates $(0, a, 0)$ and $(0, -a, 0)$ respectively as shown in the figure. The current in each of the wire is equal and along negative $z-$ axis (into the plane of the paper). The variation of magnetic field on the $x-$ axis will be approximately