Question #292024

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.


1
Expert's answer
2022-01-31T10:35:00-0500

Electric field due to charge q1q_1

E2=kq1r12E_2=\frac{kq_1}{r_1^2}

Electric Field due to charge q2q_2

E2=kq2r2E_2=\frac{kq_2}{r^2}

Net electric field sum of both charge

Enet=E1E2E_{net}=E_1-E_2

E=kq1r12kq2r22=0E=\frac{kq_1}{r_1^2}-\frac{kq_2}{r_2^2}=0 P

r1=rx,r2=r+xr_1=r-x,r_2=r+x

q1(rx)2=q2(r+x)2\frac{q_1}{(r-x)^2}=\frac{q_2}{(r+x)^2}


q2(r22rx+x2)=q1(r2+2rx+x2)q_2(r^2-2rx+x^2)=q_1(r^2+2rx+x^2)

x2(q2q1)2rx(q1+q2)r2(q2q1)x^2(q_2-q_1)-2rx(q_1+q_2)-r^2(q_2-q_1)

1.8x26.2rx1.8r21.8x^2-6.2rx-1.8r^2


1.8x26.2×0.021x1.8×0.0211.8x^2-6.2\times0.021x-1.8\times0.021

1.8x20.1302x0.03781.8x^2-0.1302x-0.0378

x=b+b24ac2ax=\frac{-b+\sqrt{b^2-4ac}}{2 a}

x=0.1302+0.13022+4×1.8×0.03782×1.8x=\frac{0.1302+\sqrt{0.1302^2+4\times1.8\times0.0378}}{2 \times1.8} x=0.185m


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