# Velocity of charged particle in a uniform electric field

• pcml100
In summary, the electric field is pushing the particle in the x-direction and the initial velocity is in the y-direction, so the final velocity is in the x-direction.

## Homework Statement

A particle of mass 0.000103 g and charge 87 mC moves in a region of space where the
electric ﬁeld is uniform and is 4.8 N/C in the x direction and zero in the y and z direction.
If the initial velocity of the particle is given by v_y = 3.2 × 10^5 m/s, v_x = v_z = 0, what is
the speed of the particle at 0.2 s?

E = E_x + E_y

a_x = (q/m)E_x
a_y = (q/m)E_y

a = a_x + a_y

v_f = V_0 + at

## The Attempt at a Solution

q = 0.087 C
m = 1.03 * 10^-7 kg
E_x = 4.8 N/C
V_0)y = 3.2 * 10^5 m/s
V_0)x = 0 m/s
V_0)z = 0 m/s
t = 0.2s

a_x = (q/m) E_x = 4054368.932 m/s^2

a_y = 0

a = 4054368.932 m/s^2

Okay use E=F/Q

Solve for F.

Now use F=ma

Solve for a

Now you have Initial V, acceleration, and t, solve for Final V.

Vf=Vo + at

pcml100 said:
q = 0.087 C
m = 1.03 * 10^-7 kg
E_x = 4.8 N/C
V_0)y = 3.2 * 10^5 m/s
V_0)x = 0 m/s
V_0)z = 0 m/s
t = 0.2s

a_x = (q/m) E_x = 4054368.932 m/s^2

a_y = 0

a = 4054368.932 m/s^2
Okay, so you've found the x-component of the acceleration. What's the x-component of the velocity, as a function of t? Then what is the x-component of the velocity when t = 0.2 s?

Another hint: Once you have both the x- and -y components of the velocity, how you do find the magnitude of the velocity (aka the speed)?

[Edit: JustinLiang beat me to the hint.]

E=F/Q
F=QE
ma=QE
a=(QE)/m=4054368.932 m/s^2

Vf=(3.2x10^5) + (4054368.932)(0.2) = 401087.3786 m/s

The system is telling me this answer is wrong. Did I miss anything?

I don't know if the problem is that the electric field is pulling in the x-direction while my initial velocity is in the y-direction.

ohhhh! so the initial velocity in the x-direction would be:

Vf = 0 + (4054368.932)(0.2) = 81087.37864 m/s

and

V = sqrt ((81087.37864)2 + (3.2x10^5)2) = 330113.8637 m/s ?

pcml100 said:
E=F/Q
F=QE
ma=QE
a=(QE)/m=4054368.932 m/s^2

Vf=(3.2x10^5) + (4054368.932)(0.2) = 401087.3786 m/s
The quoted text in red is the initial velocity in the y direction, not the x!

Keep your components separate for now.

What is vx = vx0 + axt?
I don't know if the problem is that the electric field is pulling in the x-direction while my initial velocity is in the y-direction.
That's right. That means that the particle is accelerating in the x-direction. And since the constant electric field is perpendicular to the y direction, the particle does not accelerate in the y direction.

pcml100 said:
ohhhh! so the initial velocity in the x-direction would be:

Vf = 0 + (4054368.932)(0.2) = 81087.37864 m/s

It is 810873m/s not 81087

Oh! Thank You for catching that mistake.

My answer now comes down to a final velocity of 871731.7804 m/s. Is this correct?

pcml100 said:
My answer now comes down to a final velocity of 871731.7804 m/s. Is this correct?
'Looks good to me. (A little overkill on the precision though. But yes, that's what I got.)

collinsmark said:
'Looks good to me. (A little overkill on the precision though. But yes, that's what I got.)

ha! I know, but the system wants the answer to six significant digits so I kind of have to keep EVERY digit up to the very end.

I cannot thank you both enough for your help and quick responses. Thank you so much!

JustinLiang said:
Okay use E=F/Q

Solve for F.

Now use F=ma

Solve for a

Now you have Initial V, acceleration, and t, solve for Final V.

Vf=Vo + at

Please take care not to give too much of the answer to the student asking the schoolwork question. Please ask probing questions, provide hints, find mistakes, etc. The student must do the bulk of the work. Thanks.

berkeman said:
Please take care not to give too much of the answer to the student asking the schoolwork question. Please ask probing questions, provide hints, find mistakes, etc. The student must do the bulk of the work. Thanks.

With all due respect, the input actually helped me solve the problem properly

pcml100 said:
With all due respect, the input actually helped me solve the problem properly

You mean "easily". What did you learn about how to figure out problems like this on your own? Not much from my vantage point. And helping students learn how to learn is a big goal of the PF HH forums. Please have a look at this thread, where we discuss why the PF HH rules are the way that they are:

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## What is the formula for calculating the velocity of a charged particle in a uniform electric field?

The formula for calculating the velocity of a charged particle in a uniform electric field is v = (qE/m)t, where v is the velocity, q is the charge of the particle, E is the electric field strength, m is the mass of the particle, and t is the time. This formula is known as the "equation of motion" for a charged particle in an electric field.

## How does the direction of the electric field affect the velocity of a charged particle?

The direction of the electric field does not affect the velocity of a charged particle. The velocity of the particle will always be parallel to the electric field lines, regardless of the direction of the field.

## Does the mass of a charged particle affect its velocity in a uniform electric field?

Yes, the mass of a charged particle does affect its velocity in a uniform electric field. The larger the mass of the particle, the slower its velocity will be in the same electric field. This is because the mass is a factor in the equation of motion, and a larger mass will result in a smaller velocity.

## What happens to the velocity of a charged particle if the strength of the electric field is doubled?

If the strength of the electric field is doubled, the velocity of the charged particle will also double. This is because the electric field strength is directly proportional to the velocity of the particle, according to the equation of motion.

## Can the velocity of a charged particle in a uniform electric field ever be greater than the speed of light?

No, the velocity of a charged particle in a uniform electric field can never be greater than the speed of light. The speed of light is a universal constant and cannot be exceeded by any particle, regardless of its charge or the strength of the electric field.