Answer to Question #292024 in Electricity and Magnetism for Ben

Question

Two charges lie in a line along the x axis. Charge 1 is q1 = 0.65 C and charge 2 is q2 = 2.45 C. They are each a distance of d = 0.021 m from the origin.

What is the distance on the x-axis from the origin at which the electric field will be zero. Give your answer in meters.

Answer 1

Electric field due to charge $q_1$

$E_2=\frac{kq_1}{r_1^2}$

Electric Field due to charge $q_2$

$E_2=\frac{kq_2}{r^2}$

Net electric field sum of both charge

$E_{net}=E_1-E_2$

$E=\frac{kq_1}{r_1^2}-\frac{kq_2}{r_2^2}=0$ P

$r_1=r-x,r_2=r+x$

$\frac{q_1}{(r-x)^2}=\frac{q_2}{(r+x)^2}$

$$q_2(r^2-2rx+x^2)=q_1(r^2+2rx+x^2)$$

$$x^2(q_2-q_1)-2rx(q_1+q_2)-r^2(q_2-q_1)$$

$1.8x^2-6.2rx-1.8r^2$

$$1.8x^2-6.2\times0.021x-1.8\times0.021$$

$1.8x^2-0.1302x-0.0378$

$x=\frac{-b+\sqrt{b^2-4ac}}{2 a}$

$x=\frac{0.1302+\sqrt{0.1302^2+4\times1.8\times0.0378}}{2 \times1.8}$ x=0.185m