Two spheres, solve for electric field strength

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SUMMARY

The electric field strength at the midpoint between two insulating spheres, one charged to +89.0 nC and the other to -95.0 nC, is calculated using the formula Esphere = KQ/r^2, where K is 8.99 x 10^9 N m²/C². The correct distance used for the calculation is 4.25 cm, leading to a total electric field strength of 9.16 x 10^5 N/C. Previous attempts yielded incorrect results due to miscalculations and misunderstanding of the distance between the centers of the charges.

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axgalloway
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Homework Statement


Two 2.0-cm-diameter insulating spheres have a 6.50 cm space between them. One sphere is charged to + 89.0 nC, the other to - 95.0 nC.

What is the electric field strength at the midpoint between the two spheres?


Homework Equations


Esphere = KQ/r^2
k = 8.99 * 10^9

The Attempt at a Solution



Esphere1 + Esphere2 = Etotal

(k*89*10^-9) / (3.25*10^-2)^2 + (k*95*10^-9) / (3.25*10^-2)^2
= Wrong answer: 1.57*10^6 N/C
 
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Nasty tricky wording!
Carefully sketch the spheres and mark all the distances clearly.
Remember the wording on that force formula: "distance between the centers of the charges".
 
Here was my 2nd attempt at a solution
Esphere1 + Esphere2 = Etotal

(k*89*10^-9) / (4.25*10^-2)^2 + (k*95*10^-9) / (4.25*10^-2)^2
= Wrong answer: 4.58*10^6 N/C
 
axgalloway said:
Here was my 2nd attempt at a solution
Esphere1 + Esphere2 = Etotal

(k*89*10^-9) / (4.25*10^-2)^2 + (k*95*10^-9) / (4.25*10^-2)^2
= Wrong answer: 4.58*10^6 N/C
Actually, that solution is a calculator error.
Here was my 3rd attempt at a solution (pressing the calculator correctly this time)
Esphere1 + Esphere2 = Etotal

(k*89*10^-9) / (4.25*10^-2)^2 + (k*95*10^-9) / (4.25*10^-2)^2
Correct answer = 9.16 * 10^5 N/C

Thanks for the help.
 
Last edited:

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