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A small sphere of mass m and carrying a charge q is attached to one end of an insulating thread of length ‘a’, the other end of which is fixed at (0,0) as shown in the figure. There exists a uniform electric field in the region. The minimum velocity which should be given to the sphere at (a ,0 ) in the direction shown so that it is able to complete the circle around the origin is ( There is no gravity)


A small sphere of mass m and carrying a charge q is attached to one end of an insulating thread of length ‘a’, the other end of which is fixed at (0,0) as shown in the figure. There exists a uniform electric field in the region.



The minimum velocity which should be given to the sphere at (a,0) in the direction shown so that it is able to complete the circle around the origin is ( There is no gravity)


Grade:12

1 Answers

Sumit Majumdar IIT Delhi
askIITians Faculty 137 Points
7 years ago
Dear student,
The net force acting on the sphere would be given by:
qE_{0}=\frac{mv^{2}}{a}\Rightarrow v^{2}=\frac{qE_{0}a}{m}\Rightarrow v=\sqrt{\frac{qE_{0}a}{m}}
Here the force due to the electric force results into a centripetal force due to which the sphere would move in a circular path.
Regards
Sumit

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