Charges ? q and +2 q in the figure(Figure 1) are located at x =± a . A) Determin
ID: 1429559 • Letter: C
Question
Charges ?q and +2q in the figure(Figure 1) are located at x=±a.
A) Determine the electric field at points 1 to 4. Write each field in component form. Express your answer in terms of the variables q, a , unit vectors i^, j^, and appropriate constants. E? 1 = __
B) Express your answer in terms of the variables q, a , unit vectors i^, j^, and appropriate constants. E? 2 = __
C) Express your answer in terms of the variables q, a , unit vectors i^, j^, and appropriate constants. E? 3 = __
D) Express your answer in terms of the variables q, a , unit vectors i^, j^, and appropriate constants. E? 4 =
E) Draw the four electric field vectors on the figure.
Explanation / Answer
A) Determine the directions of the fields from the charges at 1 and 4.
The E field from the -2q charge will be E2 and the E field from the other charge will be E1
At 1:
E2 makes angle with the vertical of arctan(1/2) = 26.4° so that means it is 270°-26.4° = 243.4°
E1 makes an angle of 90°+26.4° = 116.4°
+ charge fields point radially outward in all directions, - charge fields point radially inward in all directions. Both charges are the same distance from 1 and 4: r² = 5a²
E2 = 2*E1 = 2k*q/5a²
D ) At 4 the distances are the same
At the field directions are
E1 is at 243.4° and E2 is at 116.4°
So the E vectors start at the point. At 1 E1 starts at point 1 and then points up 26.4 from the vertical while E2 starts at point 1 and points down 26.4 from the vertical in quadrant 3
At point 4 E1 points down 26.4 from the vertical and E2 points up 26.4 from the vertical.in quadrant 4