One of the two small circular coils (neither having any self-inductance) is suspended with a $V$-shaped copper wire,with its plane horizontal. The other coil is placed just below the first one with its plane horizontal. Both coils are connected in series with a $dc$ supply. The coils are found to attract each other with a force. Which one of the following statements is incorrect?

  • A
    Both the coils carry currents in the same direction.
  • B
    Coils will attract each other,even if the supply is an $ac$ source.
  • C
    Force is proportional to $d^{-1}$.
  • D
    Force is proportional to $d^{-2}$.

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$A$ mass spectrometer is a device which selects particles of equal mass. An ion with electric charge $q > 0$ and mass $m$ starts at rest from a source $S$ and is accelerated through a potential difference $V$. It passes through a hole into a region of constant magnetic field $\vec B$ perpendicular to the plane of the paper as shown in the figure. The particle is deflected by the magnetic field and emerges through the bottom hole at a distance $d$ from the top hole. The mass of the particle is:

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$A$ long thin-walled pipe of radius $R$ carries a current $I$ along its length. The current density is uniform over the circumference of the pipe. The magnetic field at the center of the pipe due to the quarter portion of the pipe shown is:

Match the following:
List-$I$List-$II$
$a$. Fleming's left-hand rule$e$. Direction of induced current
$b$. Fleming's right-hand rule$f$. South pole
$c$. Clockwise current$g$. North pole
$d$. Anticlockwise current$h$. Direction of force

The correct answer is:

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