A certain charge Q is to be divided into two parts (Q-q) and q.what is the relation of Q to q if the two parts,placed a given distance apartare to have maximium coulomb repulsion?
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Two parts are Q-q and q placed at a given distance d (constant).
K = 1/4πε
Coulomb's force of repulsion: F = K * q(Q-q)/d²
dF/dq = K/d² * [Q - 2q] = 0 for maximum force
=> q = Q/2
d²F/dq² = - 2 K/d² < 0 Hence Force is maximum for q = Q/2.
K = 1/4πε
Coulomb's force of repulsion: F = K * q(Q-q)/d²
dF/dq = K/d² * [Q - 2q] = 0 for maximum force
=> q = Q/2
d²F/dq² = - 2 K/d² < 0 Hence Force is maximum for q = Q/2.
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Answer:
Explanation:
F = 1/4πε × q (Q-q)/d²
For Electrostatic Force to be maximum, dF/dq = 0
=> d/dq {1/4πε × q (Q-q)/d²} = 0
=> Q × dq/dq - d/dq × 2q = 0
=> Q - 2q = 0
=> 2q = Q
=> q = Q/2
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