Question

# GOAL Use the superposition principle to calculate the electric field due to two point charges. Consider...

GOAL Use the superposition principle to calculate the electric field due to two point charges. Consider the following figure.

The resultant electric field  at P equals the vector sum 1 + 2, where 1 is the field due to the positive charge q1and 2 is the field due to the negative charge q2.Two point charges lie along the x-axis in the x y-coordinate plane. Positive charge q1 is at the origin, and negative charge q2 is at (0.300 m, 0). Point P is at (0, 0.400 m) on the +y-axis. A dashed line from q2 to P is 0.500 mlong and makes an acute angle θwith the x-axis. Three electric field vectors start at point P.

• Vector E1 points straight up in the +y-direction.
• Vector E2 points down and right, at an acute angle θ below the horizontal, along the line from Pto q2.
• Resultant vector E points up and right, at an acute angle ϕ above the horizontal.

PRACTICE IT

Use the worked example above to help you solve this problem. Charge q1 = 6.60 µC is at the origin, and charge q2 = -4.90 µC is on the x-axis, 0.300 m from the origin (see figure).

(a) Find the magnitude and direction of the electric field at point P, which has coordinates (0, 0.400) m.

 magnitude direction

(b) Find the force on a charge of 2.00  10-8 C placed at P.
__________ N

EXERCISE

(a) Place a charge of -4.10 µC at point P and find the magnitude and direction of the electric field at the location of q2 due to q1 = 6.60 µC and the charge at P.

 magnitude N/C direction ° counterclockwise from the +x-axis

(b) Find the magnitude and direction of the force on q2.

 magnitude N direction ° counterclockwise from the +x-axis

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