Q: A water molecule is centered at the origin with its dipole moment vector $$\vec{p}$$ aligned with the x-axis. What is the magnitude and direction of the electric field at $$r = 3.00 \times 10$$^{-9}$$\ \mathrm{m} on $$the x-axis, given $$p = 6.16 \times 10$$^{-30}$$\ \mathrm{C\cdot m}$$?

$$4.1 \times 10^6$\ \mathrm{N/C}$$ along the positive x-axis.

Question 1

A point charge $$q is $$placed at the origin. What is the direction of the electric field at a point located at $$x = 0.1\ \mathrm{m} on $$the x-axis if $$q is $$negative?

Accepted Answer

The electric field points in the negative x direction.

Question 2

Two charges, $$-Q$$ and $$+4Q$$, are placed on the x-axis as shown. At which position along the x-axis is the electric field zero?

Accepted Answer

At a point to the left of $$-Q$$, where the field from $$-Q$$ and $$+4Q$$ are equal in magnitude and opposite in direction.

Question 3

A water molecule is centered at the origin with its dipole moment vector $$\vec{p}$$ aligned with the x-axis. What is the magnitude and direction of the electric field at $$r = 3.00 	imes 10$$^{-9}$$\ \mathrm{m} on $$the x-axis, given $$p = 6.16 	imes 10$$^{-30}$$\ \mathrm{C\cdot m}$$?

Accepted Answer

$$4.1 	imes 10^6$\ \mathrm{N/C}$$ along the positive x-axis.

Question 4

Which of the following best describes the y-component of the electric field at the origin due to three charges arranged as shown: one $$+2q on $$the y-axis, and two $$+q$$ charges symmetric about the y-axis?

Accepted Answer

$$E_{y} \u003c 0$$

Question 5

A thin rod of length $$l$$ with total charge $$q is $$distributed uniformly along the y-axis. What is the x-component of the electric field at point $$P on $$the x-axis at $$x_P$$?

Accepted Answer

$$E_x = \frac{1}{4\pi\$$epsilon_0$$} \int_{-l/2}^{l/2} \frac{x_P \lambda dy}{(x_P^2$ + y^2$)^{3/2}$$}$

Question 6

Consider a parallel-plate capacitor with plate area $$A$$ and separation $$d. $$What is the magnitude of the electric field between the plates?

Accepted Answer

$$E = \frac{Q}{\$$epsilon_0$$ A}$$

Question 7

A negatively charged particle is placed between the plates of a parallel-plate capacitor and moves towards the positive plate. Which statement is correct about its motion?

Accepted Answer

The particle accelerates towards the negative plate.

Question 8

Which of the following statements about electric field lines is true?

Accepted Answer

Closely spaced field lines indicate a stronger electric field.

Question 9

A permanent electric dipole is placed at rest in a uniform electric field. What happens?

Accepted Answer

The center of the dipole does not move, but the dipole starts to rotate to align with the field.

Question 10

A permanent electric dipole is placed at rest in a nonuniform electric field. What happens?

Accepted Answer

The center of the dipole starts to move toward the region of stronger field.

Question 11

Which equation gives the electric field at a distance $$r$$ from a point charge $$q$$?

Accepted Answer

$$E = \frac{1}{4\pi\$$epsilon_0$$} \frac{q}{r^2$}$$

Question 12

A semi-circular rod has $$+Q$$ distributed along the top half and $$-Q$$ along the bottom half. What is the direction of the electric field at point $$P on $$the axis of symmetry?

Accepted Answer

The field points vertically downward.

Question 13

Which of the following is true about the magnitude of the electric field at positions A, B, and C in a region where field lines are shown closely spaced at A, moderately spaced at B, and widely spaced at C?

Accepted Answer

$$E_C \u003c E_B \u003c E_A$$

Question 14

A particle with charge $$q is at$$ $$y_0 on $$the y-axis. What is the x-component of the electric field at point $$P at$$ $$x_P on $$the x-axis?

Accepted Answer

$$E_x = \frac{1}{4\pi\$$epsilon_0$$} \frac{q x_P}{(x_P^2$ + y_0$^2$$)^{3/2}$$}$$

Question 15

Which of the following is true about the magnitude of the electric field at point P in two cases: Case A (positive and negative charge) and Case B (two positive charges of equal magnitude), with P forming a right triangle with the charges?

Accepted Answer

The magnitudes are equal.

Question 16

A charged particle is placed in an electric field $$\vec{E}. $$What is the force experienced by the particle?

Accepted Answer

$$\vec{F} = q \vec{E}$$

Question 17

Which of the following statements about the direction of electric force and field is correct for a positive test charge placed in an electric field?

Accepted Answer

The force on the charge is in the direction of the electric field.

Question 18

A microwave oven heats food using electromagnetic waves. Why is it dangerous to put metal objects inside a microwave?

Accepted Answer

Metal objects can cause sparks and potentially start a fire due to the strong electric fields at sharp edges.

Electric Forces and Fields: Study Notes ch 23

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