Solving Charge in Conductors: Find Q1, Q2 & Combined Potential

In summary, the sphere with potential 27 Volt has a charge of 5.4 x 10-10 C. The sphere with potential 18 Volt has a charge of 4.8 x 10-10 C. The combined potential is 24 Volt.
  • #1
songoku
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Homework Statement


A sphere conductor of radius 18 cm has potential 27 Volt. Another sphere conductor has potential 18 Volt. Both of them are connected and the combined potential is 24 Volt. Find:
a. the charge of second sphere
b. the charge of each sphere now


Homework Equations


Q = CV
V = kQ / r

The Attempt at a Solution


a.
V1 = k.Q1 / r1
27 = 9 x 109 x Q1 / (18 x 10-2)
Q1 = 5.4 x 10-10 C

Then I don't know how to continue...:grumpy:
 
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  • #2
Try using conservation of charge.

EDIT: Are those two sphere of same radius?
 
  • #3
You can calculate also the final charge Q1' on the first sphere, as its potential is known.
As for the second sphere, kQ2/R2=18 and kQ'2/R2=24. From here, you can find the ratio Q2'/Q2. As AGNuke said, the sum of the charge on the spheres is conserved: Q1+Q2=Q1'+Q2'.

ehild
 
  • #4
AGNuke said:
Try using conservation of charge.

EDIT: Are those two sphere of same radius?

I don't know but maybe they are not

ehild said:
You can calculate also the final charge Q1' on the first sphere, as its potential is known.
As for the second sphere, kQ2/R2=18 and kQ'2/R2=24. From here, you can find the ratio Q2'/Q2. As AGNuke said, the sum of the charge on the spheres is conserved: Q1+Q2=Q1'+Q2'.

ehild

V' = k Q1' / r1
24 = 9 x 109 x Q1' / (18 x 10-2)
Q1' = 4.8 x 10-10 C

kQ2/R2=18 ; kQ'2/R2=24
So Q2'/Q2 = 24/18 = 4/3

Q1+Q2=Q1'+Q2'
5.4 x 10-10 + Q2 = 4.8 x 10-10 + 4/3 Q2
Q2 = 1.8 x 10-10 C

Q2' = 2.4 x 10-10 C


If the spheres have same radius, then the combined potential should be: (27 + 18)/2 = 45/2 V. Am I correct in this case?

Thanks
 
  • #5
songoku said:
I don't know but maybe they are not

Q2 = 1.8 x 10-10 C

Q2' = 2.4 x 10-10 C


If the spheres have same radius, then the combined potential should be: (27 + 18)/2 = 45/2 V. Am I correct in this case?

Thanks

Your solution is excellent and you are right, if the radii were the same the final voltage would be 22.5 V.

ehild
 
  • #6
OK. Thanks a lot :smile:
 

1. How do I calculate the charge of a conductor?

To calculate the charge of a conductor, you need to use the formula Q = CV, where Q is the charge, C is the capacitance, and V is the potential difference. The capacitance is a property of the conductor and can be determined by its geometry and the material it is made of. The potential difference can be measured using a voltmeter.

2. What is the difference between Q1, Q2, and combined potential?

Q1 and Q2 refer to the individual charges on two separate conductors. Combined potential refers to the total potential when the two conductors are connected, which can be calculated by adding the individual potentials of each conductor together.

3. Can I use this formula for all types of conductors?

Yes, this formula can be used for all types of conductors, as long as they have a measurable capacitance and potential difference.

4. How do I find the combined potential when the conductors are connected in parallel?

When the conductors are connected in parallel, the combined potential is equal to the potential difference of either conductor. This is because the potential difference is the same across all points in a parallel circuit.

5. Is there a limit to the value of Q1 and Q2?

There is no limit to the value of Q1 and Q2, as long as they are within the capabilities of the conductors and the potential difference is measurable. However, it is important to note that high values of charge can lead to dangerous situations, so it is important to take proper precautions when working with large charges.

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