Question

Two point particles separated by 0.7 m carry a total charge of 150 µC.

(a) If the two particles repel each other with a force of 80 N, what are the charges on each of the two particles?

q₁ = _____ µC (smaller charge)

q₂ = _____ µC (larger charge)

(b) If the two particles attract each other with a force of 80 N, what are the charges on the two particles?

q₁ = _____ µC (smaller charge)

q₂ = _____ µC (larger charge)

Answer 1

total chrge Q = q1 + q2 = 150*10-6 C  

q2 + q1 = 150*10-6 C .............. (1)

separation between two charges d = 0.7 m

a) from Coulomb's law,

the repulsive force F = kq1q2/d2 ............... (2)

where, k = 9*10^9 Nm2/C2

force F = 80 N

substitute the given data in eq (2), we get

q1q2 = Fd2/k

q1q2 = 4.36*10-9 ............ (3)

we know, (q2 + q1)2 - (q2 - q1)2 = (4q1q2)

(q2 - q1)2 = (q2 + q1)2 - (4q1q2) ............ (4)

substitute the given data in eq (4), we get

(q2 - q1)2 = 5.08*10-9

(q2 - q1) = 0.71*10-4 C

(q2 - q1) = 71.26*10-6 C ............... (5)

addind the eq (1) and (5), we get

2q2 = 150*10-6 C + 71.26*10-6 C

q2 = 110.63*10-6 C ˜ 110. 63 μC

substitute this value in eq (5), we get

q1 = 39.37*10-6 C ˜ 39.37 μC

B) total chrge Q = q2 - q1 = 150*10-6 C  

q2 - q1 = 150*10-6 C ........... (6)

the repulsive force F = kq1q2/d2

where, k = 9*109 Nm2/C2

force F = 80 N

substitute the given data in eq (2), we get

q1q2 = Fd2/k

q1q2 = 4.36*10-9  

we know, (q2 + q1)2 - (q2 - q1)2 = (4q1q2)

(q2 + q1)2 = (q2 - q1)2 + (4q1q2)

(q2 + q1) = 199.8*10-6 C ............... (7)

addind the eq (6) and (7), we get

2q2 = 150*10-6 C + 199.8*10-6 C

q2 = 174.92 μC

substitute this value in eq (7), we get

q1 = 24.88*10-6 C ˜ 24.88 μC

If the two particles attract each other, then the charges must be unlike charges.