Two identical charges having positive charges are placed 3m apart repel each other with a force of 8×10^-3n. Now charges are connected by a metallic wire they begin to repel each other with a force of 9×10^-3n. Find the initial charges on the spheres
Answers
Let q1 and q2 charges on both spheres respectively.
both charged particles are separated 3m apart. now force of repulsion between them is F = kq1q2/(3)² = 8 × 10^-3
or, 9 × 10^9 × q1q2/9 = 8 × 10^-3
or, 10^9 × q1q2 = 8 × 10^-3
or, q1q2= 8 × 10^-12 .......(1)
now, charged particles are connected by a metallic wire they begin to repel each other with a force of 9 × 10^-3 N.
due to metallic wire, charge transfer from one sphere to other untill both attains common potential or, common charges [ because both sphere sphere are identical so, common potential attains means common charge ]
then, charge on each sphere = (q1 + q2)/2
so, force between them, F = k(q1+q2)²/4(3)² = 9 × 10^-3
or, 9 × 10^9 × (q1 + q2)²/36 = 9 × 10^-3
or, (q1 + q2)² = 36 × 10^-12
or, (q1 + q2) = 6 × 10^-6 .....(2)
from equations (1) and (2),
q1 = 4 × 10^-6 C and q2 = 2 × 10^-6C and vice - versa.
Answer:
Explanation:
See the attachment given below
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