Q: Given two charges $$q_1 = 7$$ \times $$10^{-6}$$\ \mathrm{C}$$ at 0.4$$\ \mathrm{m}$$ and q_2$ = 5 \times 10$$^{-6}$$\ \mathrm{C} at$$ $$0.5\ \mathrm{m}$$ from a point $$P$$, what is the magnitude of the net electric field at $$P if $$both charges are positive and located as shown in the diagram?

$$\displaystyle 5.49 \times 10^5$\ \mathrm{N/C}$$

Q: Given $$\vec{E}_1 = 3.94 \times 10^5$ \hat{j}\ \mathrm{N/C}$$ and $$\vec{E}_2 = -1.8 \times 10^5$ \frac{3}{5} \hat{i} + 1.44 \times 10^5$ \hat{j}\ \mathrm{N/C}$$, what is the magnitude of the net electric field?

$$\displaystyle 5.49 \times 10^5$\ \mathrm{N/C}$$

Question 1

A point charge $$-2Q is $$placed at $$(0, d)$$, and a point charge $$-Q is $$placed at $$(0, -d). $$What is the net electric field at the origin due to these two charges?

Accepted Answer

$$\displaystyle \vec{E} = -\frac{3kQ}{d^2$} \hat{j}$$

Question 2

Given two charges $$q_1 = 7$$ 	imes $$10^{-6}$$\ \mathrm{C}$$ at 0.4$$\ \mathrm{m}$$ and q_2$ = 5 	imes 10$$^{-6}$$\ \mathrm{C} at$$ $$0.5\ \mathrm{m}$$ from a point $$P$$, what is the magnitude of the net electric field at $$P if $$both charges are positive and located as shown in the diagram?

Accepted Answer

$$\displaystyle 5.49 	imes 10^5$\ \mathrm{N/C}$$

Question 3

A charge $$-Q is $$placed at a point where the electric field is $$\displaystyle \vec{E}_3 = -\frac{\sqrt{2}}{2} \frac{kQ}{d^2$} \hat{i} - \frac{\sqrt{2}}{2} \frac{kQ}{d^2$} \hat{j}. $$What is the force on the charge $$-Q at $$this point?

Accepted Answer

$$\displaystyle \vec{F} = \frac{\sqrt{2}}{2} \frac{kQ^2$}{d^2$} \hat{i} + \frac{\sqrt{2}}{2} \frac{kQ^2$}{d^2$} \hat{j}$$

Question 4

If two point charges $$q_1$$ and $$q_2$$ are placed at distances $$r_1$$ and $$r_2$$ from a point $$P$$, what is the correct formula for the net electric field at $$P$$ due to both charges?

Accepted Answer

$$\displaystyle \vec{E} = \frac{k|q_1$|}{r_1$^2} \hat{r}_1 + \frac{k|q_2$|}{r_2$^2} \hat{r}_2$$

Question 5

A charge $$Q is $$placed at the origin. Another charge $$2Q is $$placed at $$(d, 0)$$, and a charge $$-Q is $$placed at $$(0, d). $$What is the $$\hat{i}$$ component of the net electric field at the origin?

Accepted Answer

$$\displaystyle -0.293 \frac{kQ}{d^2$}$$

Question 6

Given $$\vec{E}_1 = 3.94 	imes 10^5$ \hat{j}\ \mathrm{N/C}$$ and $$\vec{E}_2 = -1.8 	imes 10^5$ \frac{3}{5} \hat{i} + 1.44 	imes 10^5$ \hat{j}\ \mathrm{N/C}$$, what is the magnitude of the net electric field?

Accepted Answer

$$\displaystyle 5.49 	imes 10^5$\ \mathrm{N/C}$$

Question 7

If the net electric field at a point is $$\vec{E} = -1.08 	imes 10^5$ \hat{i} + 5.38 	imes 10^5$ \hat{j}\ \mathrm{N/C}$$, what is the direction of the field relative to the $$+x$$ axis?

Accepted Answer

$$\displaystyle 101.3^\circ$$ from $$+x$$ axis

Question 8

A charge $$Q is $$placed at $$(d, 0)$$ and a charge $$-Q at$$ $$(0, d). $$What is the direction of the net electric field at the origin?

Accepted Answer

In the third quadrant, at $$225^\circ$$ from the $$+x$$ axis

Question 9

If $$\vec{E}_3 = -\frac{\sqrt{2}}{2} \frac{kQ}{d^2$} \hat{i} - \frac{\sqrt{2}}{2} \frac{kQ}{d^2$} \hat{j}$$, what is the magnitude of $$\vec{E}_3$$?

Accepted Answer

$$\displaystyle \frac{kQ}{d^2$}$$

Question 10

A charge $$-Q is $$placed at a point where the electric field is $$\vec{E}. $$What is the direction of the force on the charge?

Accepted Answer

Opposite to the direction of $$\vec{E}$$

Question 11

If $$\vec{E}_1$$ and $$\vec{E}_2$$ are perpendicular, what is the magnitude of the net electric field $$\vec{E}$$?

Accepted Answer

$$\displaystyle |\vec{E}| = \sqrt{E_1$^2 + E_2$^2}$$

Question 12

A charge $$Q is $$placed at $$(d, 0)$$ and another $$Q at$$ $$(0, d). $$What is the angle of the net electric field at the origin with respect to the $$+x$$ axis?

Accepted Answer

$$\displaystyle 45^\circ$$

Question 13

If $$\vec{E}_1 = 3.94 	imes 10^5$ \hat{j}\ \mathrm{N/C}$$ and $$\vec{E}_2 = -1.08 	imes 10^5$ \hat{i} + 5.38 	imes 10^5$ \hat{j}\ \mathrm{N/C}$$, what is the $$\hat{i}$$ component of the net electric field?

Accepted Answer

$$\displaystyle -1.08 	imes 10^5$\ \mathrm{N/C}$$

Question 14

If $$	an \phi = -4.98$$, what is the angle $$\phi$$ from the $$-x$$ axis?

Accepted Answer

$$\displaystyle -78.6^\circ$$

Question 15

A charge $$Q is $$placed at $$(d, 0)$$ and a charge $$2Q at$$ $$(0, d). $$What is the $$\hat{j}$$ component of the net electric field at the origin?

Accepted Answer

$$\displaystyle 0.293 \frac{kQ}{d^2$}$$

Electric Field and Force Due to Point Charges: Superposition Principle and Vector Components

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