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Question

A charged particle of mars m=1 kg and charge q=2 μC is thrown from a horizontal ground at an angle of θ=45 with speed of 20 m/s. In space a horizontal electric field E=2×107 V/m exists. Find the range on horizontal ground of the projectile thrown.
Assume that gravity is vertical and g=10 m/s2

A
400 m
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B
300 m
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C
200 m
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D
100 m
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Solution

The correct option is C 200 m
Given that,
Mass of charged particle, m=1 kg
Charge of particle, q=2 μC=2×106 C
Initial speed of the particle, v=20 m/s
Horizontal electric field, E=2×107 V/m

The path of the particle will be a parabola, but the particle will accelerate along x axis also.
Let the horizontal component of the velocity is, ux=20cos45
Verticle component of the velocity, vy=20sin45

Time of flight of the projectile is
T=2uyay=2×20sin4510=22 s

Along x axis,
acceleration, a=Fm=qEm
a=2×106×2×1071=40 m/s2
So, range of the projectile,
s=ut+12at2
s=ucosθt+12at2
s=20cos45×22+12×40×(22)2
s=200 m

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