A charge $Q$ is uniformly distributed over the surface of nonconducting disc of radius $R$. The disc rotates about an axis perpendicular to its plane and passing through its centre with an angular velocity $\omega$. As a result of this rotation a magnetic field ofinduction $B$ is obtained at the centre of the disc. If we keep both the amount of charge placed on the disc and its angular velocity to be constant and vary the radius of the disc then the variation of the magnetic induction at the centre of the disc will be represented by the figure
  • A

  • B

  • C

  • D

AIEEE 2012, Diffcult
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.*

Similar Questions

  • 1
    Two long conductors, separated by a distance $d$ carry current $I_1$ and $I_2$ in the same direction. They exert a force $F$ on each other. Now the current in one of them is increased to two times and its directions is reversed. The distance is also increased to $3d$. The new value of the force between them is
    View Solution
  • 2
    Shown in the figure is a conductor carrying a current $I$. The magnetic field intensity at the point $O$ (common centre of all the three arcs) is
    View Solution
  • 3
    An electron, moving in a uniform magnetic field of induction of intensity $\vec B,$ has its radius directly proportional to
    View Solution
  • 4
    Given below are two statements

    Statement $I$ : The electric force changes the speed of the charged particle and hence changes its kinetic energy: whereas the magnetic force does not change the kinetic energy of the charged particle

    Statement $II$ : The electric force accelerates the positively charged particle perpendicular to the direction of electric field. The magnetic force accelerates the moving charged particle along the direction of magnetic field. In the light of the above statements, choose the most appropriate answer from the options given below

    View Solution
  • 5
    A vertical straight conductor carries a current vertically upwards. A point $P$ lies to the east of it at a small distance and another point $Q$ lies to the west at the same distance. The magnetic field at $P$ is
    View Solution
  • 6
     A charged particle (electron or proton) is introduced at the origin $(x=0, y=0, z=0)$ with a given initial velocity $\overrightarrow{\mathrm{v}}$. A uniform electric field $\overrightarrow{\mathrm{E}}$ and magnetic field $\vec{B}$ are given in columns $1,2$ and $3$ , respectively. The quantities $E_0, B_0$ are positive in magnitude.

    column $I$

    column $II$ column $III$
    $(I)$ Electron with $\overrightarrow{\mathrm{v}}=2 \frac{\mathrm{E}_0}{\mathrm{~B}_0} \hat{\mathrm{x}}$ $(i)$ $\overrightarrow{\mathrm{E}}=\mathrm{E}_0^2 \hat{\mathrm{Z}}$ $(P)$ $\overrightarrow{\mathrm{B}}=-\mathrm{B}_0 \hat{\mathrm{x}}$
    $(II)$ Electron with $\overrightarrow{\mathrm{v}}=\frac{\mathrm{E}_0}{\mathrm{~B}_0} \hat{\mathrm{y}}$ $(ii)$ $\overrightarrow{\mathrm{E}}=-\mathrm{E}_0 \hat{\mathrm{y}}$ $(Q)$ $\overrightarrow{\mathrm{B}}=\mathrm{B}_0 \hat{\mathrm{x}}$
    $(III)$ Proton with $\overrightarrow{\mathrm{v}}=0$ $(iii)$ $\overrightarrow{\mathrm{E}}=-\mathrm{E}_0 \hat{\mathrm{x}}$ $(R)$ $\overrightarrow{\mathrm{B}}=\mathrm{B}_0 \hat{\mathrm{y}}$
    $(IV)$ Proton with $\overrightarrow{\mathrm{v}}=2 \frac{\mathrm{E}_0}{\mathrm{~B}_0} \hat{\mathrm{x}}$ $(iv)$ $\overrightarrow{\mathrm{E}}=\mathrm{E}_0 \hat{\mathrm{x}}$ $(S)$ $\overrightarrow{\mathrm{B}}=\mathrm{B}_0 \hat{\mathrm{z}}$

    ($1$) In which case will the particle move in a straight line with constant velocity?

    $[A] (II) (iii) (S)$    $[B] (IV) (i) (S)$   $[C] (III) (ii) (R)$   $[D] (III) (iii) (P)$

    ($2$) In which case will the particle describe a helical path with axis along the positive $z$ direction?

    $[A] (II) (ii) (R)$   $[B] (IV) (ii) (R)$  $[C] (IV) (i) (S)$   $[D] (III) (iii)(P)$

    ($3$)  In which case would be particle move in a straight line along the negative direction of y-axis (i.e., more along $-\hat{y}$ )?

    $[A] (IV) (ii) (S)$   $[B] (III) (ii) (P)$   $[C]$ (II) (iii) $(Q)$   $[D] (III) (ii) (R)$

    View Solution
  • 7
    A strong magnetic field is applied on a stationary electron, then
    View Solution
  • 8
    A current of $1\,A$ is flowing on the sides of an equilateral triangle of side $4.5\times10^{-2}\,m$ . The magnetic field at the centre of the triangle will be
    View Solution
  • 9
    A charge $q$  is spread uniformly over an insulated loop of radius $r$ . If it is rotated with an angular velocity $\omega $ with respect to normal axis then the magnetic moment of the loop is
    View Solution
  • 10
    A proton accelerated by a potential difference $500\;KV$ moves though a transverse magnetic field of $0.51\;T$ as shown in figure. The angle $\theta $through which the proton deviates from the initial direction of its motion is......$^o$
    View Solution