This question is for an algebrabased class that uses the boo

This question is for an algebra-based class that uses the book PHYSICS, VOLUME II, 7TH EDITION by Douglas Giancoli:

Two point charges, 5.0 µC and -2.0 µC, are placed 5.8 cm apart on the x axis, such that the -2.0 µC charge is at x = 0 and the 5.0 µC charge is at x = 5.8 cm.

(a) At what point(s) along the x axis is the electric field zero? (If there is no point where E = 0 in a region, enter \"0\" in that box.)

(b) At what point(s) along the x axis is the potential zero? Let V = 0 at r = . (If there is no point where V = 0 in a region, enter \"0\" in that box.)

Solution

a. let us consider case x<0

k x 2x 10^-6/x^2 = k x 5 x 10^-6 /( x+5.8)^2

so, 2(x+5.8)^2 = 5x^2

so, x= 9.98 cm so answer is -9.98 cm

for case 0<x<5 answer is 0 as field can not be zero

for case x>5 cm answer is 0 as field can not be zero

b. for case x<0

k x 2x 10^-6/x = k x 5 x 10^-6/(x+5.8)

so, 2x+11.6 = 5x

so, x = 3.866 cm

so answer is -3.866 cm

for case 0<x<5

k x 2 x 10^-6/x = k x 5 x 10^-6 /(5.8-x)

so, 11.6-2x=5x

so, x= 1.657 cm

for case x>5

k x 2 x 10^-6/(x+5.8) = k x 5x 10^-6/x

so, no solution

hence answer is 0