Which of the following statements is correct?

  • A
    $A$ charged particle enters a region of uniform magnetic field at an angle $85^o$ to magnetic lines of force. The path of the particle is a circle.
  • B
    An electron and proton are moving with the same kinetic energy along the same direction. When they pass through a uniform magnetic field perpendicular to their direction of motion,they describe circular paths.
  • C
    There is no change in the energy of a charged particle moving in a magnetic field,although a magnetic force acts on it.
  • D
    Both $(B)$ and $(C)$

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$A$ conductor lies parallel to the $Z$-axis between $-1.5 \le Z < 1.5 \text{ m}$,carrying a constant current of $10.0 \text{ A}$ in the $-\hat{a}_z$ direction. For the given magnetic field $\vec{B} = 3.0 \times 10^{-4} e^{-0.2x} \hat{a}_y \text{ T}$,find the power required to move the conductor at a constant speed from $x = 0$ to $x = 2.0 \text{ m}$ in a time interval of $5 \times 10^{-3} \text{ s}$. Assume the motion is parallel to the $X$-axis. ........... $\text{W}$

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The unit of magnetic flux density (or magnetic induction) is:

Two charged particles $A$ and $B$,each of charge $+e$ and masses $12 \, amu$ and $13 \, amu$ respectively,follow a circular trajectory in chamber $X$ after passing through a velocity selector as shown in the figure. Both particles enter the velocity selector with a speed of $1.5 \times 10^6 \, ms^{-1}$. $A$ uniform magnetic field of strength $1.0 \, T$ is maintained within the chamber $X$ and in the velocity selector,directed into the plane ($-z$ direction).

Match List-$I$ with List-$II$.
List-$I$List-$II$
$(A)$ Permeability of free space$(I) \ [M L^2 T^{-2}]$
$(B)$ Magnetic field$(II) \ [M T^{-2} A^{-1}]$
$(C)$ Magnetic moment$(III) \ [M L T^{-2} A^{-2}]$
$(D)$ Torsional constant$(IV) \ [L^2 A]$

Choose the correct answer from the options given below:

The adjoining figure shows a very long semi-cylindrical conducting shell of radius $R$ carrying a current $i$. An infinitely long straight current-carrying conductor is lying along the axis of the semi-cylinder. If the current flowing through the straight wire is $i_0$,then the force per unit length on the conducting wire is

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