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The relation between voltage sensitivity (${\sigma _V}$) and current sensitivity $({\sigma _i})$ of a moving coil galvanometer is (Resistance of Galvanometer = $G$)
A rectangular loop of wire, supporting a mass $m$, hangs with one end in a uniform magnetic field $\vec B$ pointing into the plane of the paper. $A$ clockwise current is set up such that $i> mg/Ba,$ where $a$ is the width of the loop. Then
An electron, moving along the $x-$ axis with an initial energy of $100\, eV$, enters a region of magnetic field $\vec B = (1.5\times10^{-3}T)\hat k$ at $S$ (See figure). The field extends between $x = 0$ and $x = 2\, cm$. The electron is detected at the point $Q$ on a screen placed $8\, cm$ away from the point $S$. The distance $d$ between $P$ and $Q$ (on the screen) is :......$cm$ (electron's charge $= 1.6\times10^{-19}\, C$, mass of electron $= 9.1\times10^{-31}\, kg$)
A wire carrying a current $i$ is placed in a uniform magnetic field in the form of the curve $y = a\sin \,\left( {\frac{{\pi x}}{L}} \right)\,0 \le x \le 2L.$ The force acting on the wire is
A $2 \mathrm{~A}$ current carrying straight metal wire of resistance $1 \Omega$, resistivity $2 \times 10^{-6} \Omega \mathrm{m}$, area of cross-section $10 \mathrm{~mm}^2$ and mass $500 \mathrm{~g}$ is suspended horizontally in mid air by applying a uniform magnetic field $\vec{B}$. The magnitude of $B$ is__________.$\times 10^{-1} \mathrm{~T}\left(\right.$ given, $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ )
An infinitely long wire, located on the $z$-axis, carries a current $/$ along the $+z$-direction and produces the magnetic field $\vec{B}$. The magnitude of the line integral $\int \vec{B} \cdot d l$ along a straight line from the point $(-\sqrt{3} a, a, 0)$ to $(a, a, 0)$ is given by [ $\mu_0$ is the magnetic permeability of free space.]