IV. Two small spheres, each carrying a net positive charge, are separated by 0.4

Question

IV. Two small spheres, each carrying a net positive charge, are separated by 0.400m. You have been asked to perform measurements that will allow you to determine the charge on each sphere. You set up a coordinate system with one sphere (charge q1) at the origin and the other sphere (charge q2) at x = +0.400 m. Available to you are a third sphere with net charge q3 = 4.00 * 10-6 C and an apparatus that can accurately measure the location of this sphere and the net force on it. First you place the third sphere on the x-axis at x = 0.200 m; you measure the net force on it to be 4.50 N in the tx-direction. Then you move the third sphere to x = +0.600 mand measure the net force on it now to be 3.50 N in the +x- direction. A. Calculate q1 and q2. B. What is the net force (magnitude and direction) on q3 if it is placed on the x- axis atx-0.200 m? C. At what value ofx (other than,-(q) could q3 be placed so that the n force on it is zero? et

Explanation / Answer

(A) at x = 0.2 m,

F = k q1 q3 / 0.2^2 - k q2 q3 / 0.2^2

4.50 = (9 x 10^9 x 4 x 10^-6 / 0.2^2) (q1 - q2)

q1 - q2 = 5 x 10^-6 .... (i)

at x = 0.60 m

3.50 = (9 x 10^9 x 4 x 10^-6)[q1/0.6^2 + q2/0.2^2]

q1 + 9q2 = 35 x 10^-6 ... (ii)

solving, q1 = 8 x 10^-6 C and q2 = 3 x 10^6 C

(B) F = (9 x 10^9 x 4 x 10^-6 x 10^-6)(-8/0.2^2 - 3/0.6^2)

F = - 7.5 N

magnitude = 7.5 N

direction = to the -ve axis

(C) that will be in between the charges,

F = k q1 q3 / x^2 - k q2 q3/(0.4 - x)^2 = 0

(0.4 - x)/x = sqrt(3/5) = 0.775

x = 0.225 m ...Ans

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

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