Question 673: Electrostatics & Capacitance

Question

A body having specific charge 8 $$\mu$$C/g is resting on a frictionless plane at a distance 10 cm from the wall (as shown in the figure). It starts moving towards the wall when a uniform electric field of 100 V/m is applied horizontally towards the wall. If the collision of the body with the wall is perfectly elastic, then the time period of the motion will be _______________ s.

Accepted Answer

Given,
q = 8$$\mu$$C/g = 8 $$	imes$$ 10
$$-$$6
C/g = 8 $$	imes$$ 10
$$-$$3
C/kg
s = 10 cm = 0.1 m $$\Rightarrow$$ E = 100 V/m
We know that, acceleration, a = $${{force(F)} \over {mass(m)}}$$
$$\Rightarrow$$ a = $${{qE} \over m}$$ [$$\because$$ F = qE]
= $${{8 	imes {{10}^{ - 6}} 	imes 100} \over {{{10}^{ - 3}}}}$$ = 0.8 ms
$$-$$2
As per question, when electric field is switched on, the body strikes to the wall and then returns back.
For one oscillation,
s = ut + $${1 \over 2}$$ at
2
$$\Rightarrow$$ 0.1 = $${1 \over 2}$$ $$	imes$$ 0.8 t
2
[$$\because$$ u = 0]
$$\Rightarrow$$ 0.2 = 0.8 t
2
$$\Rightarrow$$ $${2 \over 8}$$ = t
2
$$\Rightarrow$$ t
2
= $${1 \over 4}$$ $$\Rightarrow$$ t = $${1 \over 2}$$
$$	herefore$$ Time period = 2 $$	imes$$ $${1 \over 2}$$ = 1 s
Therefore, if the collision of the body is perfectly elastic, the time period of motion will be 1s.

Electrostatics & Capacitance

Integer / Numeric Answer Type