Question

Two charges, -1.90uC and 4.45uC are placed at x=0cm and x=5.50cm, respectively.

1) At what point along the x-axis is the electric field zero?
2) At what points along the x-axis is the potential zero? Let V=0 at r=8

Answer 1

let us specify the location as a distance x fromq₁
distance between two charges d = 20 cm
q ₁ = 1.90μC = 3 *10 ^-6 C
q ₂ = 4.45μC = 7 *10 ^-6 C
setting the magnitudes of the individual fields equaland solving for x
E₁= E₂
k q₁ /x² = k q₂/ ( x+d ) ²
1 / x²= (q₂ /q₁ ) / ( x + d ) ²
q ₂ / q₁ = 4.45/ 1.90 =2.34
1 / x² =2.34 / ( x + d )²
1 / x=(√2.34) / x+ d
x+ d = 1.53 x
d= 0.53 x
x= 5.5*10^-2/ 0.53
= 0.0359 m

= 3.59 cm