29: Problem 29.41

PART A: 
Determine the magnitude and direction of the electric field at point 1 in the figure

SOLUTION: 
I like to start out by naming the rings
A=0V
B=25V
C=50V
D=75V
point 1 is on ring C and 1 cm away from rings B & D
A formula to determine the potential along this line would be 2500d, where d is the distance from ring A in meters
since E(x) is the negative derivative of V(x), E(x) = -2500 V/m, or in terms of vectors, E = 2500 V/m down

PART B:
Determine the magnitude and direction of the electric field at point 2 in the figure.

SOLUTION:
similar solution, except along this line the rings are much closer together, like 0.5 cm apart. 
a function for this line going towards the A ring is 5000d. Take the derivative again and it's 5000 V/m. Remember that it is also negative so in terms of vectors, it would be pointing up. E = 5000 V/m up