b) What is the initial charge q1 on the first sphere? Answer in units of µC. Sho
ID: 1512032 • Letter: B
Question
b) What is the initial charge q1 on the first sphere? Answer in units of µC.
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Two identical small metal spheres with q1 > 0 and |q1| > |q2| attract each other with a force of magnitude 95.3 mN when separated by a distance of 2.02m. The spheres are then brought together until they are touching, enabling the spheres to attain the same final charge q. After the charges on the spheres have come to equilibrium, they spheres are separated so that they are again 2.02 m apart. Now the spheres repel each other with a force of magnitude 18.107 mN. What is the final charge on the sphere on the right? The value of the coulomb constant is 8.98755 x 10^9 N. m^2/C^2. Answer in units of muC.Explanation / Answer
After touching each other, they both have same charge now, q
Electrostatic Force, F = k*q^2/r^2
18.107 * 10^-3 = (8.98755 * 10^9 * q^2)/(2.02)^2
q = 2.87 * 10^-6 C
q = 2.87 uC
Final Charge on the sphere, q = 2.87 uC
(b)
Total Charge = 2*q = 2*2.87 uC = 5.74 uC
Now,
q1 + q2 = 5.74 uC -------1
Electrostatic Force, F = (k*q1*q2)/r^2
95.3 * 10^-3 = (8.98755 * 10^9 * q1*q2)/(2.02)^2
q1*q2 = 4.33 * 10^-11 --------2
Using eq 1 & 2,
q1 = 10.05 uC
q2 = - 4.31 uC
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