Work done to move a test charge

In summary, a test charge of +1.0*10^-6 C is placed 40cm from a charged sphere of 3.2*10^-3 C. The work required to move the test charge from a point 1.0*10^2 m away from the sphere is calculated using the formula W=delta Ee and is found to be 71.712 J. To determine the electrons that were gained or lost from the test subject to create the charge, the test charge can be multiplied by the inverse of the elementary charge (1.60217646 × 10-19) or divided by 6.242 × 10^18 e using Millikan's relationship.
  • #1
ND3G
79
0
A test charge of +1.0*10^-6 C is 40cm from a charged sphere of 3.2*10^-3

How much work is required to move it there from a point 1.0*10^2 m away from the sphere?

GIVEN:
q1 = +1.0*10^-6 C
q2 = 3.2*10^-3 C
r1 = 1.0*10^2 m
r2 = 0.40 m

Required:
W

Analysis:
Ee=(k*q1*q2)/r
delta Ee=E2-E1
W=delta Ee

Solution:

179.99712 J

Am I on the right track here? It just doesn't seam right to me for some reason. Also, since the charged sphere does not clearly specify that it is a positive or negative charge, should I assume it is postive?
 
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  • #2
I am assuming by Ee, you mean Electrical potential energy, correct?

If this is the case then I believe you are on the right track. G01
 
Last edited:
  • #3
Can someone help me with this question. please. i have tried all i could but i am nowhere arround the right answer. :(
 
  • #4
I don't know where the 179.99712 J came from. By my calculation k*q1*q2 is (9.0x10^9)*(1.0*10^-6)*(3.2*10^-3)=28.8 According to this Ee2 = 28.8/0.4=72 and Ee1 = 28.8/100 = 0.288
 
  • #5
rojasharma said:
Can someone help me with this question. please. i have tried all i could but i am nowhere arround the right answer. :(
I got the answer as 179.75 J, which is pretty close to the OP's answer. You should post your attempt so we can check it for you.
 
  • #6
I don't think the OP's answer is correct. Defennder do you mind sharing how you got that number?

Here's what I got

GIVEN:
q1 = +1.0*10^-6 C
q2 = 3.2*10^-3 C
r1 = 1.0*10^2 m
r2 = 0.40 m

E1 = (k*q1*q2) / r1
= (9.0*10^9*3.2*10^-3*1*10^-6)/(100m)
= 0.288 J

E2 = (k*q1*q2) / r2
= (9.0*10^9*3.2*10^-3*1*10^-6)/(0.4m)
= 72 J

W=deltaE= E2 - E1
= 72J - 0.288J
= 71.712J

Therefore 71.712J of work is required.

Can anyone comment on this please? I honestly don't get how they got a number close to 180J
 
  • #7
jwj11 said:
Therefore 71.712J of work is required.

Can anyone comment on this please?
Looks good to me.
 
  • #8
Well this thread has been inactive for some time. Looking back I think my error and probably that of the OP was to square 0.4m Otherwise I think the correct answer should be about -71.6J.
 
  • #9
For this very same question above, how would I determine the electrons that were gained or lost from the test subject to create the charge?
 
  • #10
saiyaex said:
For this very same question above, how would I determine the electrons that were gained or lost from the test subject to create the charge?
Assuming the test object was originally neutral, every time you remove one electron the charge remaining will increase by one elementary charge (which is the magnitude of the charge on an electron). What's the charge on an electron?
 
  • #11
1.60217646 × 10-19
 
  • #12
do I multiply the test charge with 6.242 × 10^18 e using millikan's relationship?
 
  • #13
saiyaex said:
do I multiply the test charge with 6.242 × 10^18 e using millikan's relationship?
That works. Realize that multiplying by that number is the same as dividing by the electron charge.
 
  • #14
oh okay! simple enough. thanks a bunch.
 

What is work done to move a test charge?

Work done to move a test charge is the energy required to move a test charge from one point to another against an electric field.

How is the work done to move a test charge calculated?

The work done to move a test charge is calculated by multiplying the magnitude of the charge by the potential difference between the two points.

What is the unit of measurement for work done to move a test charge?

The unit of measurement for work done to move a test charge is joules (J).

Does the work done to move a test charge depend on the path taken?

No, the work done to move a test charge is independent of the path taken. It only depends on the initial and final positions of the test charge.

What does a positive or negative value for work done to move a test charge indicate?

A positive value for work done to move a test charge indicates that energy is being supplied to the test charge, while a negative value indicates that energy is being released by the test charge.

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