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Question

The electric potential varies in space according to the relation V=3x+4y. A particle of mass 0.1kg starts from rest from point (2,3.2) under the influence of this field. The charge on the particle is +1μC. Assume V and (x,y) are in S.I. units
The time taken to cross the x - axis is

A
20 s
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B
40 s
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C
20 s
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D
400 s
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Solution

The correct option is D 400 s
V=3x+4y
We know that the relation between V and E is given by
E=[δVδx^i+δVδy^j+δVδz^k]
Ex=δVδx^i
Ex=3Vm1
Similarly, Ey=δVδy^j
Ey=4 Vm1 (downward)
Only this y component of electric field is responsible for the particle to cross x-axis.
The acceleration of particle along y- axis will be
ay=qEym
We know
Sy=ut+12at2
Sy=12qEymt2
Sy=3.2 m (given)
On putting all values from above we will get t=400 s


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