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6. Free-Response Questions Four point charges, each with a magnitude $|q| = 6.0$ nC, are fixed at different locations along the perimeter of a square of side length $d = 4.0$ cm. The origin of the xy-plane is fixed at the top right corner of the square. d d/2 q q O y q q x d/4 a. Draw and label a diagram that includes all electric field vectors at point O. Include x- and y-components if necessary. b. Calculate the magnitude and direction of the net electric field $\vec{E}$ at point O. c. If a charge $Q = -3$ µC is placed at point O, calculate the magnitude and direction of the electric force $\vec{F}_\text{on } Q$. Bonus: Charge Q now accelerates off to an infinite distance away from the sources. If a fifth charge $q'$ is now placed at the location $\vec{r} = d(\hat{i} + \hat{j})$, determine its charge that would create a net electric field of xero at point O.

          6.
Free-Response Questions
Four point charges, each with a magnitude $|q| = 6.0$ nC, are fixed at different
locations along the perimeter of a square of side length $d = 4.0$ cm. The origin of the
xy-plane is fixed at the top right corner of the square.
d
d/2
q
q
O
y
q
q
x
d/4
a. Draw and label a diagram that includes all electric field vectors at point O.
Include x- and y-components if necessary.
b. Calculate the magnitude and direction of the net electric field $\vec{E}$ at point O.
c. If a charge $Q = -3$ µC is placed at point O, calculate the magnitude and
direction of the electric force $\vec{F}_\text{on } Q$.
Bonus: Charge Q now accelerates off to an infinite distance away from the
sources. If a fifth charge $q'$ is now placed at the location $\vec{r} = d(\hat{i} + \hat{j})$,
determine its charge that would create a net electric field of xero at point O.

6.
Free-Response Questions
Four point charges, each with a magnitude |q| = 6.0 nC, are fixed at different
locations along the perimeter of a square of side length d = 4.0 cm. The origin of the
xy-plane is fixed at the top right corner of the square.
d
d/2
q
q
O
y
q
q
x
d/4
a. Draw and label a diagram that includes all electric field vectors at point O.
Include x- and y-components if necessary.
b. Calculate the magnitude and direction of the net electric field E⃗ at point O.
c. If a charge Q = -3 µC is placed at point O, calculate the magnitude and
direction of the electric force F⃗on Q.
Bonus: Charge Q now accelerates off to an infinite distance away from the
sources. If a fifth charge q' is now placed at the location r⃗ = d(î + ĵ),
determine its charge that would create a net electric field of xero at point O.

Added by Erin T.

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