Point charges of 8.00 n C are situated at each of three corners of a square whos
ID: 2120371 • Letter: P
Question
Point charges of 8.00nC are situated at each of three corners of a square whose side is 0.350m .
A)What is the magnitude of the resultant force on a point charge of -3.50micro C
if it is placed at the center of the square? (N)
B)What is the direction of the resultant force on a point charge of -3.50 micro C
if it is placed at the center of the square?
C) What is the magnitude of the resultant force on a point charge of -3.50 micro C
if it is placed at the vacant corner of the square? (N)
D)What is the direction of the resultant force on a point charge of -3.50 micro C
if it is placed at the vacant corner of the square?
Explanation / Answer
Use the relation: E = kq/r^2 where k=9e9, q = 9e-9, so kq =81
If the four corners of the square are labeled 1,2,3,4 moving clockwise with 1 being the top, left most corner. Corner 3 is the empty corner at the lower right of the square.
Each charge is (1/2)*sqrt( 0.15^2+0.15^2)=0.106m from the charge at the center of the square.
Therefore, the E fields due to charges 2 and 4 cancel at the center of the square because they are equal but in opposite directions.
The distance from each corner to the center of the square is 0.106m. The net E field at the center of the square is due to the charge at corner 1:
k*9e-9/0.106^2 = 81/0.106^2 = 7200 V/m and it's direction is 45 degrees beneath the horizontal.
F = qE = -4e-6*9e9*9e-9/0.106^2 = 2.88e-2N =2.88x10^-2 N <-----------------
If the negative charge is at corner 3:
Charges 2 and 3 provide E fields down and to the right (vertical and horizontal). Charge 1 provides an E field at negative 45 degrees.
k*9e-9 = 81.
The distance from charges at corners 2 and 4 to corner 3 is 0.15m (given).
The distance to corner 3 from corner 1 is sqrt(0.15^+0.15^2)=0.212m
We must sum the horizontal and vertical components to determine the net E field.
Horizontal: 81/0.15^2 + 81cos(-45)/0.212^2 = 4872.8 V/m
Vertical : 81/0.15^2 + 81sin(-45)/0.212^2 = 4872.8 V/m
The magnitude of the resultant E field at corner 3 is 6891.2 V/m
The force on the -4uC charge at corner 3 is then 4e-6*6891.2 = 2.76e-2N <-----