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Question

In a certain region uniform electric field E and uniform magnetic field B  are present in opposite directions. A particle of mass m and of charge q enters in this region with a velocity v at an angle θ from the magnetic field. The time after which the speed of the particle would be minimum is equal to :


Your Answer
A
2πmqB
Your Answer
B
mvsinθqE
Correct Answer
C
mvcosθqE
Your Answer
D
mvqE

Solution

The correct option is D mvcosθqE
The charge experiences a retarding force F=qE along x axis. Retardation =qEm
It is clear that the speed of the particle will be minimum when its component of velocity along the direction of electric field is zero.
Thus, using the equation of motion.
v=u+at
0=vcosθqEmt
or t=mvcosθqE

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