Velocity Selector

Q. A particle having a charge of $10.0\mu C$ and mass $1\mu g$ moves in a circle of radius 10 cm under the influence of a magnetic field of induction 0.1T. When the particle is at a point P, a uniform electric field is switched on so that the particle starts moving along the tangent with a uniform velocity. The electric field is

1. 0.1 V/m
2. 1.0 V/m
3. 10.0 V/m
4. 100 V/m

Q. Two identical charged spheres suspended from a common point by two massless strings of lengths $l$, are initially at a distance $d(d<<l)$ apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity $v$. Which of the following correctly represent the variation of $v$ as a function of the distance $x$ between the spheres.

1. $v\propto x^{-\frac{1}{2}}$
2. $v\propto x^{-1}$
3. $v\propto x^{-\frac{1}{2}}$
4. $v\propto x^{\frac{1}{2}}$

Q. A block of mass m and charge q is released from rest on incline plane of angle $\theta$ and coefficient of friction $\mu$. $\theta$ is greater than angle of repose. A magnetic field perpendicular to page inwards also exist as shown in figure, then

1. Speed of block increases linearly.
2. Maximum speed attained by block is $\frac{mg}{\mu qB}(sin\theta -\mu cos\theta )$
3. Speed of block increases exponentially and reaches infinity
4. Time to reach maximum speed is infinity

Q. A particle having a charge of $10.0\mu C$ and mass $1\mu g$ moves in a circle of radius 10 cm under the influence of a magnetic field of induction 0.1T. When the particle is at a point P, a uniform electric field is switched on so that the particle starts moving along the tangent with a uniform velocity. The electric field is

1. 0.1 V/m
2. 1.0 V/m
3. 10.0 V/m
4. 100 V/m