Question

The electrical potential function for an electrical field directed parallel to the x-axis is shown in Fig. The intervals in which the magnitude of the electric field in the x-direction is maximum are :

• A. $-2\le x\le 0,4\le x\le 8,and0\le x\le 2$
• B. $-2\le x\le 0,and0\le x\le 2$
• C. $-2\le x\le 0,2\le x\le 4,and4\le x\le 8$
• D. $0\le x\le 2,and4\le x\le 8$

Answer 1

Answer: (C)

$-2\le x\le 0,2\le x\le 4,and4\le x\le 8$

$E_r=-\frac{\Delta V}{\Delta r};E_x=-\frac{\Delta V}{\Delta x}$
For $-2\le x\le 0,E_x=-\frac{(10-0)}{[0-(-2\left)\right]}=-5N{C}^{-1}$
For $0\le x\le 2,E_x=0$
For $2\le x\le 4,E_x=-\frac{[20-10]}{[4-2]}=-5N{C}^{-1}$
For $4\le x\le 8,E_x=-\frac{[0-20]}{[8-4]}=5N{C}^{-1}$