A proton moving with a velocity, $2.5 \times {10^7}\,m/s$, enters a magnetic field of intensity $2.5\,T$ making an angle ${30^o}$ with the magnetic field. The force on the proton is
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A current $I$ flows around a closed path in the horizontal plane of the circle as shown in the figure. The path consists of eight arcs with alternating radii $r$ and $2r$. Each segment of arc subtends equal angle at the common centre $P.$ The magnetic field produced by current path at point $P$ is
A $3.0\; cm$ wire carrying a current of $10 \;A$ is placed inside a solenoid perpendicular to its axis. The magnetic field inside the solenoid is given to be $0.27\; T$. What is the magnetic force on the wire?
A particle of charge $q$ and mass $m$ moving with a velocity $v$ along the $x$-axis enters the region $x > 0$ with uniform magnetic field $B$ along the $\hat k$ direction. The particle will penetrate in this region in the $x$-direction upto a distance $d$ equal to
A particle of charge $q$ and mass $m$ moving with a velocity $v$ along the $x$-axis enters the region $x > 0$ with uniform magnetic field $B$ along the $\hat k$ direction. The particle will penetrate in this region in the $x$-direction upto a distance $d$ equal to
Consider a thin metallic sheet perpendicular to the plane of the paper moving with speed $'v'$ in a uniform magnetic field $B$ going into the plane of the paper (See figure). If charge densities ${\sigma _1}$ and ${\sigma _2}$ are induced on the left and right surfaces, respectively, of the sheet then (ignore fringe effects)
In the circuit, shown the galvanometer $G$ of resistance $60\, \Omega$ is shunted by a resistance $r=0.02\, \Omega$. The current through $R$ (in $ohm$) is nearly $1\, A$. The value of resistance $R$ (in $ohm$) is nearly (in $\Omega$)
Two coaxial solenoids of different radii carry current $I$ in the same direction. Let $\;{\overrightarrow {\;F} _1}$ be the magnetic force on the inner solenoid due to the outer one and $\;{\overrightarrow {\;F} _2}$ be the magnetic force on the outer solenoid due to the inner one. Then
A symmetric star conducting wire loop is carrying a steady state current $\mathrm{I}$ as shown in figure. The distance between the diametrically opposite vertices of the star is $4 a$. The magnitude of the magnetic field at the center of the loop is
$A$ and $B$ are two concentric circular conductors of centre $O$ and carrying currents ${i_1}$ and ${i_2}$ as shown in the adjacent figure. If ratio of their radii is $1 : 2$ and ratio of the flux densities at $O$ due to $A$ and $B$ is $1 : 3$, then the value of ${i_1}/{i_2}$ is