Q: Light of wavelength $$\lambda = 655\ \mathrm{nm}$$ illuminates a single slit and forms a diffraction pattern on a screen $$2.4\ \mathrm{m}$$ away. The first dark fringe is formed $$3.77\ \mathrm{mm}$$ away from the central bright fringe. What is the width $$W of $$the slit?

$$W = 4.4 \times 10$$^{-3}$$\ \mathrm{m}$$

Q: What is the magnitude of the electric field $$E at $$the origin, O, due to the three charges at the vertices of the triangle?

$$|E| = 1.5 \times 10^6$\ \mathrm{N/C}$$

Q: Three charges are assembled along the X-axis as shown below. All three charges have $$Q = +2\ \mathrm{mC}$$ and are equally spaced with $$d = 0.5\ \mathrm{m}. $$What is the electric potential at the location of the central charge due to the other two charges?

$$71.92 \times 10^3$\ \mathrm{V}$$

Question 1

A car crosses the line connecting two radio transmitters at right angles, each transmitting identical signals in phase. The car's radio picks up a maximum net signal at a certain point. If the transmitters are 450 m apart, what is the longest possible wavelength $$\lambda_{max} of $$the radio waves that produces this maximum?

Accepted Answer

$$\lambda_{max} = 300\ \mathrm{m}$$

Question 2

Green light of wavelength $$\lambda = 532\ \mathrm{nm}$$ illuminates a pair of slits separated by $$d = 0.42\ \mathrm{mm}. An $$interference pattern is observed on a screen placed a distance $$L$$ away. What is the distance $$L if $$the width of the central bright spot of the interference pattern is $$1.5\ \mathrm{cm}$$?

Accepted Answer

$$L = 15\ \mathrm{m}$$

Question 3

Which of these wavelengths of light would produce a larger central bright spot than green light ($$\lambda = 532\ \mathrm{nm}) in a $$double-slit experiment?

Accepted Answer

Red-orange ($$635\ \mathrm{nm})$$

Question 4

Light of wavelength $$\lambda = 655\ \mathrm{nm}$$ illuminates a single slit and forms a diffraction pattern on a screen $$2.4\ \mathrm{m}$$ away. The first dark fringe is formed $$3.77\ \mathrm{mm}$$ away from the central bright fringe. What is the width $$W of $$the slit?

Accepted Answer

$$W = 4.4 	imes 10$$^{-3}$$\ \mathrm{m}$$

Question 5

If light of a different wavelength $$\lambda = 531\ \mathrm{nm} is $$used with the same single-slit setup, the first dark fringe will:

Accepted Answer

Move closer to the central bright fringe

Question 6

For what wavelength $$\lambda of $$incident light such that the fifth-order ($$m = 5) $$bright fringe can still be seen in a double-slit experiment with slit separation $$d = 0.42\ \mathrm{mm}$$ and screen distance $$L = 2.4\ \mathrm{m}$$?

Accepted Answer

$$\lambda = 540.5\ \mathrm{nm}$$

Question 7

Two sister stars are found to emit the same wavelength $$\lambda = 230\ \mathrm{nm}$$ and are located a distance $$d = 3.75 	imes 10$$^{17}$$\ \mathrm{m}$$ away from Earth. The stars are estimated to be separated by $$s = 4.5 	imes 10$$^{11}$$\ \mathrm{m}. $$What minimum diameter $$D_{min} of $$telescope lens is needed to resolve their images?

Accepted Answer

$$D_{min} = 2.3\ \mathrm{m}$$

Question 8

Three point-charges are placed at the vertices of an equilateral triangle of side $$2\ \mathrm{cm} as $$shown: $$q_1 = +1$$\ \mu\mathrm{C}$$, q_2$ = -5\ \mu\mathrm{C}$$, $$q_3 = +1$$\ \mu\mathrm{C}$$. What is the magnitude of the net electric force F$ on the charge q_1$?

Accepted Answer

$$|F| = 194\ \mathrm{N}$$

Question 9

What is the direction of the electric field at the origin, O, due to the three charges placed at the vertices of an equilateral triangle?

Accepted Answer

$$\uparrow$$

Question 10

What is the magnitude of the electric field $$E at $$the origin, O, due to the three charges at the vertices of the triangle?

Accepted Answer

$$|E| = 1.5 	imes 10^6$\ \mathrm{N/C}$$

Question 11

Compare the magnitude of the two charges $$q_A$$ and $$q_B$$ shown in the field line diagram. Which one is greater?

Accepted Answer

$$|q_A| \u003e |q_B|$$ – There are more electric field lines connected to $$q_A$$

Question 12

Where is the magnitude of the electric field greater – at point A or at point B?

Accepted Answer

At point B – density of electric field lines is greater at point B

Question 13

What would the direction of force on a positive test charge placed at the midpoint of the two charges be, if the two charges were positive?

Accepted Answer

To the right

Question 14

A charge $$Q = -3\ \mu\mathrm{C} in a $$uniform electric field $$E = 5 	imes 10^6$\ \mathrm{N/C}$$ moves from point A to point B along the solid line shown (A: $$x=0$$, $$y=4\ \mathrm{m}$$; B: $$x=3\ \mathrm{m}$$, $$y=0). $$What is the change in potential experienced by the charge as it moves from A to B?

Accepted Answer

$$\Delta V = -20\ \mathrm{MV}$$

Question 15

What is the change in the electrical potential energy of the system as the charge moves from A to B?

Accepted Answer

$$\Delta U = 60\ \mathrm{J}$$

Question 16

Three charges are assembled along the X-axis as shown below. All three charges have $$Q = +2\ \mathrm{mC}$$ and are equally spaced with $$d = 0.5\ \mathrm{m}. $$What is the electric potential at the location of the central charge due to the other two charges?

Accepted Answer

$$71.92 	imes 10^3$\ \mathrm{V}$$

Question 17

What is the potential energy of this configuration of three charges?

Accepted Answer

$$1.8 	imes 10^3$\ \mathrm{J}$$

Question 18

If the charges all had $$Q = -2\ \mathrm{mC}$$, would the potential energy increase, decrease or remain the same?

Accepted Answer

Remain the same

Question 19

A parallel-plate capacitor is constructed with circular plates of radius $$0.051\ \mathrm{m}$$ separated by $$0.25\ \mathrm{mm}$$, and the space between the plates is filled with dielectric constant $$k. $$When the charge on the capacitor is $$1.8\ \mu\mathrm{C}$$, the potential difference between the plates is $$115.0\ \mathrm{V}. $$What is the magnitude of electric field between the two plates?

Accepted Answer

$$4.6 	imes 10^5$\ \mathrm{V/m}$$

Question 20

Find the value of $$k ($$dielectric constant) for the parallel-plate capacitor described above.

Accepted Answer

$$k = 5.4$$

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