A) Two conducting spheres have identical radii. Initially they have charges of o

Question

A)
Two conducting spheres have identical radii. Initially they have charges of opposite sign and unequal magnitudes with the magnitude of the positive charge larger than the magnitude of the negative charge. They attract each other with a force of 0.281 N when separated by 0.3 m.
Initial
The spheres are suddenly connected by a thin conducting wire, which is then removed.
Connected
Now the spheres repel each other with a force of 0.031N.
Final
What is the magnitude of the positive charge?
Answer in units of C.
B)
What is the negative charge?
Answer in units of C. A)
Two conducting spheres have identical radii. Initially they have charges of opposite sign and unequal magnitudes with the magnitude of the positive charge larger than the magnitude of the negative charge. They attract each other with a force of 0.281 N when separated by 0.3 m.
Initial
The spheres are suddenly connected by a thin conducting wire, which is then removed.
Connected
Now the spheres repel each other with a force of 0.031N.
Final
What is the magnitude of the positive charge?
Answer in units of C.
B)
What is the negative charge?
Answer in units of C. A)
Two conducting spheres have identical radii. Initially they have charges of opposite sign and unequal magnitudes with the magnitude of the positive charge larger than the magnitude of the negative charge. They attract each other with a force of 0.281 N when separated by 0.3 m.
Initial
The spheres are suddenly connected by a thin conducting wire, which is then removed.
Connected
Now the spheres repel each other with a force of 0.031N.
Final
What is the magnitude of the positive charge?
Answer in units of C.
B)
What is the negative charge?
Answer in units of C.

Explanation / Answer

Given,

F1 = -0.281 N ; d = 0.3 m ; F2 = 0.031 N

We know that the force of attraction or repulsion between two charges is given by

F = k q1q2/r^2

F1 = -0.281 N = k q1q2/r^2

q1q2 = -0.281 x 0.3^2/9 x 10^9 = -28.1 x 10^-12 C^2

q2 = -28.1 x 10^-12/q1

When they repel,

k(q1 + q2)^2/d^2 = F2 = 0.031 N

q1 + q2 = sqrt(0.031 x 0.3^2/9 x 10^9) = 0.56 x 10^-6 C

q1 + -28.1 x 10^-12/q1 = 0.56 x 10^-6

q1^2 - 0.56 x 10^-6 q1 - 28.1 x 10^-12 = 0

q1 = 5.59 x 10^-6 C

q2 = -28.1 x 10^-12/q1 = -28.1 x 10^-12/5.59 x 10^-6 = -5.03 x 10^-6 C

Hence, q1 = 5.59 x 10^-6 C and q2 = -5.03 x 10^-6 C.

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