It\'s a question related to physics2 Unit: Coulomb\'s Law Can you please show al

Question

It's a question related to physics2 Unit: Coulomb's Law
Can you please show all the steps,
Thanks, Chapter 21 Problem 030 In the figure partides 1 and 2 are fixed in place on an x axis, at a separation of L 9.30 cm. Their charges are a +e and ga -27e. Partide 3 with charge +3e is to be placed on the line between partides 1 and 2, so that they produce a net electrostatic force F3net on it. (a) At what coordinate should partice 3 be placed to minimize the magnitude of that force? (b) What is that minimum magnitude? (a) Number Units (b) Number Units

Explanation / Answer

let, distance b/w particle 1 and 3 = x

so, force on q3 due to q1

F31= k*e*3e / x^2

F31 = 9*10^9*3e^2 / x^2 = 27*10^9*e^2 / x^2

force on q2 due to q3

F32 = 9*10^9*27e*3e / (L-x)^2 = 729*10^9 / (L-x)^2

net force on q3 is

Fnet = F31 + F32 = 9*10^9*e^2 [3 / x^2 + 81 / (L-x)^2]

dFnet / dx = 9*10^9*e^2 [-3 / x^3 + 81 / (L-x)^3] = 0

3 / x^3 = 81 / (L-x)^3

multiply with 9 both the sides

27 / x^3 = 729 / (L-x)^3

3 / x = 9 / (L-x)

x = L / 4 = 9.30 / 4

x = 2.32 cm

(b)

minimum magnitude of force

Fmin = 9*10^9*e^2 [3 / x^2 + 81 / (L-x)^2]

Fmin = 9*10^9*e^2 [3 / (L/4)^2 + 81 / (L-L/4)^2]

Fmin = 9*10^9 * (1.6*10^(-19))^2 * [48 / L^2 + 1296/9*L^2]

Fmin = 23.04*10^(-29) * [48 / (0.093)^2 + 1296/(0.837)^2]

by solving

Fmin = 17.04*10^(-25) N

answer

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.