As shown in the figure on the left, a positive test charge
placed exactly halfway between a ball of charge +Q and a
second ball of unknown charge experiences a net force directed
right. When the second ball is removed from the situation, as in
the figure on the right, the force experienced by the test charge
increases by a factor of 1.60. What is the sign and magnitude of
the charge on the second ball?Please explain how you got the answer!
here,
the initial force on the test charge , F1 = K * Q * q /(r^2) - K * Q2 * q /r^2
F1 = K * q /r^2 * ( Q - Q2) . .....(1)
when the second charge is removed
the force on the test charge , F2 = 1.6 * F1
K * Q * q /r^2 = 1.6 * F1 ....(2)
from (1) and (2)
1/1.6 = (Q - Q2) /Q
Q = 1.6 * Q - 1.6 * Q2
Q2 = 0.375 Q
the charge on second ball is 0.375 Q
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