Q. 485.0( 1 Vote )

# A particle of mass 1g and charge 2.5 × 10–4 C is released from rest in an electric field of 1.2 × 104 N C–1.(a) Find the electric force and the force of gravity acing on this particle. Can one of these forces be neglected in comparison with the other for approximate analysis?(b) How long will it take for the particle to travel a distance of 40 cm?(c) What will be the speed of the particle after travelling this distance?(d) How much is the work done by the electric force on the particle during this period?

Given:
Mass of the particle : m= 1g = 10-3 kg
Charge of the particle: q = 2.5 × 10–4 C
Electric Field: E = 1.2 × 104 N C–1
Distance travelled : s = 40 cm = 0.4 m
Initial velocity: u = 0
Formula used:

(a)
When a charge q moves in an uniform electric field E, it experiences an electric force Fe.
Fe = qE
substituting the values we get,
Fe = 3N
Force of gravity would be:
Where m is the mass of the particle and g is the acceleration due to gravity.

Since the mass of the particle is very low, force due to gravity can be neglected.
(b)
From Newton’s Second Law,
F=ma
where a is the acceleration of the body and m is the mass.
acceleration of the particle is:

Here, s is the distance travelled, u is the initial velocity, t is the time required to travel s, and a is the acceleration of the particle.
Substituting we get,

It will take 0.0163 seconds for the particle to travel a distance of 40 cm.
(c)
Using another equation of motion
Here v is the final velocity of the particle,u is the initial velocity of the particle, a is the acceleration and s is the distance travelled by the particle.
Substituting we get,

After travelling 40cm the speed of the particle will be 48.9 m/s.
(d)
We know that,
Work=Force×Displacement
Thus work done by the electric force:
W = F × s
W = 3× 0.4
W = 1.2 J

Hence , work of 1.2 J is being done by the electric force on the particle.

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