A boy is holding a smooth, hollow and non-conducting pipe vertica… - Vidyadip

Question

A boy is holding a smooth, hollow and non-conducting pipe vertically with charged spherical ball of mass 10 g carrying a charge of +10 mC inside it which is free to move along the axis of the pipe. The boy is moving the pipe from East to West direction in the presence of magnetic field of 2T. With what minimum velocity, should the boy move the pipe such that the ball does not move along the axis. Also determine the direction of the magnetic field.

✓

Answer

Given
$B=2 T, q=10 mC$, mass of the ball $=10^{-2} kg, g=9.8 m / s ^2$ Magnetic force $(q v B \sin \theta)=$ gravitational force $( mg )$ $
v=\frac{m g}{q B \sin \theta}
$
For min. velocity $\sin \theta=1$

$\begin{aligned} v & =\frac{m g}{q B \sin \theta}=v=\frac{m g}{q B} \\ & =\frac{10^{-2} \times 9.8}{10^{-2} \times 2} m / s \\ & =4.9 m / s \\ & v=4.9 m / s ^2\end{aligned}$
As force is in upward direction so from Fleming’s Left-hand rule, magnetic field will be along North to South.

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