Question

Three charges q1 = 1 C, q2 = – 2 q1, and q3 = 3 q2 are placed along the x-axis. Charge q2 is at equal distance from other two charges. The charge q1 is at the origin (0, 0) and charge q3 is at (100, 0) cm.
(a) Show the positions of all the charges in a suitable diagram.
(b) Find the magnitude of electric fields E1 and E3 at a point P (50, 0).
(c) Find the magnitude of resultant electric field at P and its direction.
(d) Find the work done in bringing charge q1 to (0, 0) from infinity.
(e) Find the total potential at point P.

Answer 1

2)For magnitude of electric field we have formula

$$E=k\frac{q}{r^2}$$

where

$$k=9\cdot 10^9$$

then

$$E_1=9\cdot 10^9 \cdot \frac{1\cdot 10^{-6}}{0.25}=36(kV/m)$$

$$E_2=9\cdot 10^9 \cdot \frac{3\cdot 10^{-6}}{0.25}=108(kV/m)$$

3)resultant field

$$\vec{E}=\vec{E_1}+\vec{E_3}$$ $$E=E_3-E_1$$ $$E=72(kV/m)$$

4)Potential in dot (0,0)

$$P_1=\frac{kq_3}{1}-\frac{kq_2}{0.5}=-9(kV)$$

Work is

$$A=q_1(P_1-P(infinity))$$

$$E=10^{-6}\cdot (9000-0)=9(mJ)$$

5)Total potential in point P

$$P_p=\frac{kq_1}{0.5}+\frac{kq_3}{0.5}=72(kV)$$