Download App
Two charged particles of mass $m$ and charge $q$ each are projected from origin simultaneously with same speed $V$ in transverse magnetic field. If ${\vec r_1}$ and ${\vec r_2}$ are the position vectors of particles (with respect to origin) at $t = \frac{{\pi m}}{{qB}}$ then the value of  ${\vec r_1}.{\vec r_2}$ at that time is
  • A${\left( {\frac{{mv}}{{qB}}} \right)^2}$
  • B$\frac{1}{2}{\left( {\frac{{mv}}{{qB}}} \right)^2}$
  • C$2{\left( {\frac{{mv}}{{qB}}} \right)^2}$
  • D$4{\left( {\frac{{mv}}{{qB}}} \right)^2}$
Medium
art

Download our app
and get started for free

Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Download App

Similar Questions

  • 1
    In order to pass $10\,\%$ of main current through a moving coil galvanometer of $99\, ohm$, the resistance of the required shunt is ............ $\Omega $
    View Solution
  • 2
    A galvanometer having a coil resistance of $60\,\,\Omega$ shows full scale deflection when a current of $1.0$ $amp$ passes through it. It can be converted into an ammeter to read currents upto $5.0$ $amp$ by
    View Solution
  • 3
    A proton and a deutron ( $\mathrm{q}=+\mathrm{e}, m=2.0 \mathrm{u})$ having same kinetic energies enter a region of uniform magnetic field $\vec{B}$, moving perpendicular to $\vec{B}$. The ratio of the radius $r_d$ of deutron path to the radius $r_p$ of the proton path is:
    View Solution
  • 4
    A galvanometer whose resistance is $120\,\Omega $ gives full scale deflection with a current of $0.05\, A$ so that it can read a maximum current of $10\, A$. A shunt resistance is added in parallel with it. The resistance of the ammeter so formed is .............. $\Omega $
    View Solution
  • 5
    $\alpha$ particle is revolving in radius $r$ with frequency $f$ then find value of magnetic dipole moment.
    View Solution
  • 6
    The magnetic moment of a current $(i)$ carrying circular coil of radius $(r)$ and number of turns $(n)$ varies as
    View Solution
  • 7
    A loop in form of four connected semi-circular wires carrying current $I$ lies in the $x-y$ plane as shown in the figure. The unit vector $\hat k$ is coming out of the plane of the paper. The magnetic moment of the current loop is
    View Solution
  • 8
    A coaxial cable having radii $a, b$ and $c$ carries equal and opposite currents of magnitude $i$ the inner and outer conductors. What is the magnitude of the magnetic induction at point $P$ outside of the cable at a distance $r$ from the axis?
    View Solution
  • 9
    Two moving coil meters $M_1$ and $M_2$ having the following particulars :-
    $R_1 = 10\,\Omega , N_1 = 30, A_1 = 3.6\times10^{-3}\, m^2, B_1 = 0.25\, T$
    $R_2 = 14\,\Omega , N_2 = 42, A_2 = 1.8\times10^{-3}\, m^2, B_2 = 0.50\, T$
    (The spring constants are identical for the two meters). Determine the ratio of voltage sensitivity of $M_2$ and $M_1$
    View Solution
  • 10
    A proton and an $\alpha$ -particle, having kinetic energies $K _{ p }$ and $K _{\alpha},$ respectively, enter into $a$ magnetic field at right angles.

    The ratio of the radii of trajectory of proton to that of $\alpha$ -particle is $2: 1 .$ The ratio of $K _{ p }: K _{\alpha}$ is :

    View Solution