Part (a) of the figure shows two charged particles fixed in place on an x axis w

Question

Part (a) of the figure shows two charged particles fixed in place on an x axis with separation L. The ratio q1/q2 of their charge magnitudes is 4.00. Part (b) of the figure shows the x component Enet,x of their net electric field along the x axis just to the right of particle 2. The x axis scale is set by xs = 32.4 cm. (a) At what value of x > 0 is Enet,x maximum? (b) If particle 2 has charge -5e, what is the value of that maximum? Assume e = 1.602 × 10-19 C.

Part (a) of the figure shows two charged particles fixed in place on an x axis with separation L. The ratio q1/q2 of their charge magnitudes is 4.00. Part (b) of the figure shows the x component Enetx of their net electric field along the x axis just to the right of particle 2. The x axis scale is set by xs = 32.4 cm, (a) At what value of x > 0 is Eneex maximum? (b) If particle 2 has charge-5e, what is the value of that maximum? Assume e = 1.602 x 10-19 C. +g x(cm) Nm UnitT m (a) Number TTo.34 Unit N/C (b) NumberT3.6e-8

Explanation / Answer

Ex =- k q2 / x^2 + k q1 / (x + L)^2 = 0

(x + L) / x = sqrt(q1/q2) = 2

Ex is zero at x = 2 x 32.4 / 3 = 21.6 cm

L = x = 21.6 cm

putting, d(Ex)/dx = 0

=> -2 k q2 / x - 2 k q1 / (x + L) = 0

q2 / x = q1/ (x + L)

x + L / x = q1 / q2 = 4

x + 21.6 = 4x

x = 7.2 cm .......Ans

(b) q2 = -5e

q1 = - 20e

Ex = - k q2 / x^2 + k q1 / (x + L)^2

= - k(-5e) / 0.072^2 + k(-20e) / (0.072 + 0.216)^2

=(9 x 10^9 x 1.6 x 10^-19) ( 964.51 - 241.13)

= 1.04 x 10^-6 N/C

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