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Three point charges q1, q2, q3 are in line at equal distances. q2 and q3 are opposite in sign. Find the magnitude and sign of q1, if net force on q3 is zero

Three point charges q1, q2, q3 are in line at equal distances. q2 and q3 are opposite in sign. Find the magnitude and sign of q1, if net force on q3 is zero

Grade:12

3 Answers

Arun
25750 Points
6 years ago
Dear student
 
Let Q1 be a test positive charge, since charges of Q2 and Q3 are opposite in sign, there exists an attractive force between them. One point to be kept in mind here is that the net force on Q3 must be 0 as given in the problem. In order to keep force on Q3 be 0, the force between Q1 and Q3 must be force of repulsion as we already have attractive force between Q2 and Q3
Now to satisfy the equilibrium position, the two forces must balance each other.
KQ1Q3/4R2 = -KQ2Q3/R2….. (distance between Q1 and Q3 is 2R).
Q1 = -4Q2
Hence charge of Q1 is opposite to that of Q2 and same as that of Q3
ankit singh
askIITians Faculty 614 Points
3 years ago
Let Q1 be a test positive charge, since charges of Q2 and Q3 are opposite in sign, there exists an attractive force between them. One point to be kept in mind here is that the net force on Q3 must be 0 as given in the problem. In order to keep force on Q3 be 0, the force between Q1 and Q3 must be force of repulsion as we already have attractive force between Q2 and Q3
Now to satisfy the equilibrium position, the two forces must balance each other.
KQ1Q3/4R2 = -KQ2Q3/R2….. (distance between Q1 and Q3 is 2R).
Q1 = -4Q2
Hence charge of Q1 is opposite to that of Q2 and same as that of Q3
 
Amalraj Aaryan
26 Points
2 years ago
Q2​ and Q3​ are equal is magnitude but opposite in sign.
∴Q2​ and Q3​ experience attractive force due to each other. Now Q1​ must have sign of Q3​ to repel it so that Net force on Q3​ is zero
⇒r2−kQ2​Q3​​=(2r)2k(Q1​)Q3​​
 
 
⇒Q1​=−4Q2​
 
 
⇒Q1​=4∣Q3​∣
 
as ∣Q2​∣=∣Q3​∣
 
 

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