Charge to Mass Ratio Calculation for Object

In summary, an object with mass of 8.668 * 10^-13 kg is deflected downward a vertical distance of 6235565 m/s from its original direction of motion when it passes through an electric field between two parallel metal plates.
  • #1
koolmerliner
3
0

Homework Statement


A small object with mass m, charge q, and initial speed v0 = 6.00×10^3 m/s is projected into a uniform electric field between two parallel metal plates of length 26.0 cm(Figure 1) . The electric field between the plates is directed downward and has magnitude E = 600 N/C . Assume that the field is zero outside the region between the plates. The separation between the plates is large enough for the object to pass between the plates without hitting the lower plate. After passing through the field region, the object is deflected downward a vertical distance d = 1.35 cm from its original direction of motion and reaches a collecting plate that is 56.0 cm from the edge of the parallel plates. Ignore gravity and air resistance.

Part A
Calculate the object's charge-to-mass ratio, q/m.

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Homework Equations


E = F/q
E=kq/r^2
kinematics

The Attempt at a Solution


I solved for q by using E = kq/r^2[/B]
Er^2/k = q
(600 N/C)(.26 m)^2 / 9x10^9 Nm^2/C^2 = q
q = 4.51 * 10^-9 C

My plan for mass is

Eq = F = ma
Eq/a = m

Using Kinematics
Solving for time t

x - x0 =1/2(v0x + vx)t
2(x-x0)/(v0x + vx) = t
2(.56m)/(2 * 6 *10^3 m/s) = t
t = 9.33*10^-5 s


Solving for Acceleration y-axis ay

y = y0 + v0yt + (1/2)ayt^2
2(y - y0 - v0yt)/t^2 = ay
2(.56m)/t^2 = ay
ay = 3127478 m/s


Eq/a = m

m = 8.668 * 10^-13 kg

q/m = 5203 wrong answer


 
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  • #2
koolmerliner said:
2(.56m)/t^2 = ay
The acceleration only applies while between the plates. Break the problem into two parts.
 
  • #3
And while you do what haruspex suggested, consider that the E-field in which the particle travels is not kq/r^2, which is the field generated by a point charge, but a uniform field of 600 N/C generated by external charges on the plates.
 
  • #4
I tried solving for Vy(in plates) which is equal to V0y and Vy (outside the plates)
y-y0 = 1/2(2Vy)t
(-0.0135m)/t = Vy
t = 5 * 10^-5 s (outside the from 26 to 56) calculated wrong in post
Vy = (-0.0135m)/t = -270 m/s

Now solving for t (x=0 to x=.26m)
(x-x0) = (1/2)(v0x + v0x)t
(.26m)/(6.00 * 10^3 m/s) = t
t = 4.33*10^-5 s

ay = (-270m/s)/ t
ay = 6235565 m/s^2
 
Last edited:
  • #5
A "previous question" is often an unreliable source. Here you don't have a line of charge, just a moving charge in a uniform electric field. The electric field in the line of charge question does not have the same dependence on space coordinates (it looks different if you draw field lines in space) as a uniform electric field, which is what you have here. Therefore, it is incorrect to use the line-of-charge of expression where it does not apply and expect to make sense out of it.

I have not done the math yet to see if your number for ay is correct. Assuming that it is, can you find an expression for ay in terms of the charge q, the external electric field E and the mass m?
 
  • #6
kuruman said:
A "previous question" is often an unreliable source. Here you don't have a line of charge, just a moving charge in a uniform electric field. The electric field in the line of charge question does not have the same dependence on space coordinates (it looks different if you draw field lines in space) as a uniform electric field, which is what you have here. Therefore, it is incorrect to use the line-of-charge of expression where it does not apply and expect to make sense out of it.

I have not done the math yet to see if your number for ay is correct. Assuming that it is, can you find an expression for ay in terms of the charge q, the external electric field E and the mass m?

ay = qE/m
 
  • #7
Right. Now look at the equation. What quantity are you trying to find and how can you write it in terms of known quantities?
 

Related to Charge to Mass Ratio Calculation for Object

What is the charge to mass ratio of an object?

The charge to mass ratio of an object is defined as the ratio of its electric charge to its mass. It is usually denoted by q/m and has the unit of coulombs per kilogram (C/kg).

How is the charge to mass ratio of an object calculated?

The charge to mass ratio of an object can be calculated by measuring the charge of the object and its mass, and then dividing the charge by the mass. This can be done using various techniques such as the Millikan oil drop experiment or the Thomson's cathode ray tube experiment.

What is the significance of the charge to mass ratio in physics?

The charge to mass ratio is an important quantity in physics as it helps in determining the nature of particles and their behavior in electric and magnetic fields. It is also used in various calculations related to electricity and magnetism, such as calculating the force on a charged particle in a magnetic field.

How does the charge to mass ratio vary for different objects?

The charge to mass ratio can vary significantly for different objects depending on their composition and physical properties. For example, the charge to mass ratio of an electron is much higher than that of a proton, due to the electron's smaller mass.

Can the charge to mass ratio of an object change?

Yes, the charge to mass ratio of an object can change if its charge or mass is altered. For example, if an object gains or loses electrons, its charge to mass ratio will also change. Similarly, if an object's mass changes, its charge to mass ratio will also be affected.

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