Two point charges, 5.0 µC and -2.0 µC, are placed 5.0 cm apart on the x axis, su

Question

Two point charges, 5.0 µC and -2.0 µC, are placed 5.0 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 = 5.0 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.)

x < 0:______________

0 < x < 5.0 cm:______________

5.0 cm < x________________

(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.)

x < 0:________________

0 < x < 5.0 cm:_________

5.0 cm < x__________

x < 0:________________

0 < x < 5.0 cm:_________

5.0 cm < x__________

Explanation / Answer

part a )

kq/x^2 = kq/(d-x)^2

5/x^2 = 2/(0.05-x)^2

5x^2 -0.5 + 0.0125 = 2x^2

3x^2 - 0.5 + 0.0125 = 0

x = 0.136 m , 0.03 m

x <0 = 0

0<x<5 = 3 cm

5 < x = 13.6 cm

part b )

kq/|x| = kq/|x-5|

5/|x| = 2/|x-5|

5|x-5| = 2|x|

5x-25 = 2x

3x = 25

x = 8.33 cm

5x-25 = -2x

7x = 25

x = 25/7 = 3.57

x < 0 = 0

0< x < 5. = 3.57

5 < x = 8.33

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