The potential as a function of position x is shown in the gr

The potential as a function of position x is shown in the graph in the figure. Which statement about the electric field is true? The electric field is zero at x = 0, its magnitude is at a maximum at x = 5 cm, and the field is directed to the right there. The electric field is zero at x = 5 cm, its magnitude is at a maximum at x = 0, and the field is directed to the right there. The electric field is zero at x = 0, its magnitude is at a maximum at x = 15 cm, and the field is directed to the left there. The electric field is zero at x = 10 cm, its magnitude is at a maximum at x = 5 cm, and the field is directed to the left there. Student Learning Outcome:1: At the end of this course, the successful student will be able to: -Calculate the Electric Field and Electric Potential in the region around simple configurations of Electric Charges and Conducting Surfaces, (Tested with questions 13-17) (For Questions 13-13) Two positive point charges +4.00 MuC and +2.00 Mu are placed at the opposite comers of a rectangle in the x-y plane as shown in the figure. (k = 1/4Pi Epsilon 0 = 8.99 Times 10^9 N. m^2/C^2) What is the potential at point A (relative to infinity) due to these charges? What is the potential at point B (relative to infinity) due to these charges? What is the electric Held at point A due to these charges? (Give E_x assuming x points to the right, E_y assuming y points up. and E, assuming z points out of the paper towards you.)

Solution

around 0 cm the potential is flat in an small range. Electric field is rate of change of potential dv/dx which is zero around x=0 cm

hence E is 0 at x= 0cm

the curve is steep at x=5 cm and the slope is maximum hence E is maximum at x= 5cm Point s to the left are at higher potential and points to the right are at lower potential. A +ve charge would move to the right at x=5 cm and field is directed to the right.

answer A:

13) potential at A   = 8.99e+9(4e-6/0.8 +2e-6/0.4)

                             = 8.99 e+4 V

14) potential at B   = 8.99e+9(4e-6/0.4 +2e-6/0.8)

                             = 11.24 e+4 V

15 )

          Ex = -8.99e+9*4e-6/0.8² = -56.187e+3 N/C

          Ey = -8.99e+9*2e-6/0.4² = 112.375 e+3 N/C

           Ez =0