Anonymous
Anonymous asked in Science & MathematicsPhysics · 3 months ago

# Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of 0.119 N...?

Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of 0.119 N when their center-to-center separation is 71.9 cm.

The spheres are then connected by a thin conducting wire. When the wire is removed, the spheres repel each other with an electrostatic force of 0.0325 N. Of the initial charges on the spheres, with a positive net charge, what was (a) the negative charge on one of them and (b) the positive charge on the other? (Assume the negative charge has smaller magnitude.)

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• NCS
Lv 7
3 months ago

electrostatic force F = kQq / d²

where k = 8.99e9 N·m²/C²

first condition:

-0.119 N = 8.99e9N·m²/C² * Q * q / (0.719m)²

Q*q = -6.84e-12 C²

second condition:

0.0325 N = 8.99e9N·m²/C² * Q'² / (0.719m)²

Q'² = 1.87e-12 C²

Q' = 1.367e-6 C

and so the total charge present is Q_tot = 2.734e-6 C = Q + q

and so

q = 2.734e-6C - Q

Q*(2.734e-6C - Q) = -6.84e-12 C²

which has roots at

Q = -1.58e-6 C = -1.58 µC ◄ initial negative

and Q = 4.32e-6 C = 4.32 µC ◄ initial positive

• JOHN
Lv 7
3 months ago