a particle that has a charge of +12.8E-19 C and a mass of 8.0E-27kg is moving along the +x axis at a constant speed of 2.0E10 m/s. it then enter a region where the eletric field of 300 N/C is directed along thr +x axis. calculate the particles displacement after it has been accelrated for a time o 2.5 microseconds.
C= colulombs
To calculate the particle's displacement after it has been accelerated for a certain time, we need to use the equation of motion:
s = ut + (1/2)at^2
Where:
s is the displacement
u is the initial velocity
a is the acceleration
t is the time
In this case, the particle is accelerated by the electric field. The force experienced by a charged particle in an electric field is given by:
F = qE
Where:
F is the force
q is the charge of the particle
E is the electric field strength
The acceleration can be calculated using Newton's second law, which states that force is equal to mass times acceleration:
F = ma
We can rearrange this equation to solve for acceleration:
a = F/m
Given:
Charge (q) = +12.8E-19 C
Mass (m) = 8.0E-27 kg
Electric field (E) = 300 N/C
Time (t) = 2.5 microseconds = 2.5E-6 s
First, calculate the acceleration:
a = F/m
= (qE)/m
= [(12.8E-19 C)(300 N/C)]/(8.0E-27 kg)
Next, calculate the displacement using the equation of motion:
s = ut + (1/2)at^2
= (2.0E10 m/s)(2.5E-6 s) + (1/2)(a)(2.5E-6 s)^2
By substituting the values, we can calculate the displacement.