Q: Two decorative copper balls are 45.0 cm apart. Each ball has a mass of 0.0240 kg. Determine the number of electrons that should be transferred from one ball to the other to create an attractive force between the balls of magnitude 8000 N. (Treat the charged balls like point charges. Elementary charge $$e = 1.60 \times 10$$^{-19}$$ C, Coulomb's constant k = 8.99$$ \times $$10^9 N$$·m²/C²)

$$2.65 \times 10$$^{15}$$ electrons

Q: A copper pipe is 5.0 m long. The outer diameter is 5.125 inches, while the inner diameter is 4.805 inches. What is the resistance of the pipe when measured (i) along its length (ii) along its wall thickness? (Assume each area acts like an equipotential surface.)

i) $$5.29 \times 10$$^{-5}$$\ \Omega ii$$) $$3.53 \times 10$$^{-11}$$\ \Omega$$

Q: A circular conductor with a radius of $$2.50\ \mathrm{cm} is $$placed in a uniform magnetic field of $$1.23\ \mathrm{T}$$ decreasing gradually at a rate of $$0.450\ \mathrm{T/s}. $$Calculate the magnitude of the induced electric field in the conductor.

$$5.63 \times 10$$^{-3}$$\ \mathrm{V/m}$$

Q: Tests on an inductor show that a self-induced emf of magnitude $$0.185\ \mathrm{V} is $$generated when the current is increased at a rate of $$0.580\ \mathrm{A/s}. $$The inductor has 550 turns. Determine the mean magnetic flux in each turn when the inductor draws a current of $$0.770\ \mathrm{A}.$$

$$4.47 \times 10$$^{-4}$$\ \mathrm{Wb}$$

Question 1

Two decorative copper balls are 45.0 cm apart. Each ball has a mass of 0.0240 kg. Determine the number of electrons that should be transferred from one ball to the other to create an attractive force between the balls of magnitude 8000 N. (Treat the charged balls like point charges. Elementary charge $$e = 1.60 	imes 10$$^{-19}$$ C, Coulomb's constant k = 8.99$$ 	imes $$10^9 N$$·m²/C²)

Accepted Answer

$$2.65 	imes 10$$^{15}$$ electrons

Question 2

Calculate the electric field 2 meters away from a charged conductor with a charge of 5 C. (Assume Coulomb's constant $$k = 8.99 	imes 10^9$ N·m²/C²)

Accepted Answer

$$22475$$ \ \mathrm{N/C}$

Question 3

Two parallel plates form a capacitor with a plate area of $$12.0\ \mathrm{cm}^2$$ and a separation distance of $$1.20\ \mathrm{mm}. $$The plates are charged to a net charge of $$\pm 0.708\ \mu\mathrm{C}. (i) $$Calculate the electric field strength between the plates. (ii) Find the electric potential difference between the plates.

Accepted Answer

(i) $$96.0\ \mathrm{MV/m} (ii$$) $$80\ \mathrm{kV}$$

Question 4

Given a capacitor with an initial electric field strength $$E_0$$, and a dielectric constant of 4 is introduced, what is the new electric field strength?

Accepted Answer

$$\frac{E_0$}{4}$$

Question 5

A copper pipe is 5.0 m long. The outer diameter is 5.125 inches, while the inner diameter is 4.805 inches. What is the resistance of the pipe when measured (i) along its length (ii) along its wall thickness? (Assume each area acts like an equipotential surface.)

Accepted Answer

i) $$5.29 	imes 10$$^{-5}$$\ \Omega ii$$) $$3.53 	imes 10$$^{-11}$$\ \Omega$$

Question 6

Two electric kettles have resistances of $$9.60\ \Omega$$ and $$12.0\ \Omega. $$They are plugged in parallel to a $$110\ \mathrm{V}$$ outlet socket. Determine the combined power output of the kettles.

Accepted Answer

$$2830\ \mathrm{W}$$

Question 7

In which condition will a wire carrying current not produce a magnetic field?

Accepted Answer

When the current in the wire is zero.

Question 8

A current $$I_0$$ flows uniformly through the cross-sectional area of an extended horizontal hollow cylindrical conductor with an inner radius $$R_A$$ and an outer radius $$R_B. A $$point $$P is $$located at a distance $$r$$ from the central axis and in a plane perpendicular to it. Determine the expression for the magnetic field for (i) $$r  R_B.$$

Accepted Answer

i) $$B=0 
ii$$) $$B=\frac{\mu_0$}{2\pi r} \left[I_0$ \frac{r^2$ - R_A^2$}{R_B^2$ - R_A^2$}\right]$$ 
iii) $$B=\frac{\mu_0$ I_0$}{2\pi r}$$

Question 9

A rod is bent into a semi-circular shape with a radius of 0.5 m. A coil of 1500 turns carrying a current of 2A is wrapped uniformly around it. Which diagram best represents the magnetic field's shape in this partial toroid?

Accepted Answer

Image 2

Question 10

A circular conductor with a radius of $$2.50\ \mathrm{cm} is $$placed in a uniform magnetic field of $$1.23\ \mathrm{T}$$ decreasing gradually at a rate of $$0.450\ \mathrm{T/s}. $$Calculate the magnitude of the induced electric field in the conductor.

Accepted Answer

$$5.63 	imes 10$$^{-3}$$\ \mathrm{V/m}$$

Question 11

Tests on an inductor show that a self-induced emf of magnitude $$0.185\ \mathrm{V} is $$generated when the current is increased at a rate of $$0.580\ \mathrm{A/s}. $$The inductor has 550 turns. Determine the mean magnetic flux in each turn when the inductor draws a current of $$0.770\ \mathrm{A}.$$

Accepted Answer

$$4.47 	imes 10$$^{-4}$$\ \mathrm{Wb}$$

Question 12

In a real-world AC circuit containing a capacitor, why is it important to understand phasor relationships?

Accepted Answer

To predict and control the timing of voltage and current for efficient power distribution.

Question 13

An engineer is testing a $$3.0\ \mathrm{k}\Omega$$ resistor in a lab by connecting it to a $$240\ \mathrm{V}$$ rms AC power supply. Determine the peak current flowing through the resistor.

Accepted Answer

$$0.17\ \mathrm{A}$$

Question 14

A team is launching a new television channel and needs to determine the broadcasting wavelength ranges. What are the specific wavelength ranges for (a) VHF (Very High Frequency) band, spanning from 30 MHz to 300 MHz, and (b) UHF (Ultra High Frequency) frequencies ranging from 470 MHz to 700 MHz?

Accepted Answer

(a) VHF: $$1\ \mathrm{m} - 10\ \mathrm{m}$$; (b) UHF: $$0.43\ \mathrm{m} - 0.64\ \mathrm{m}$$

Question 15

A light source hangs from one corner of a room. Calculate the value of $$	heta if $$the light is directed to a wall before reflecting at the midpoint of the floor. (Refer to the diagram provided.)

Accepted Answer

$$26.6^\circ$$

Question 16

During a laboratory-based course, a system of two polarizing films is used to verify Malus' law. The two films have their polarization axes inclined at $$40^\circ to $$each other. A collimated beam of unpolarized light of intensity $$5\ \mathrm{mW/m}^2 is $$sent into the system. Calculate the transmitted intensity through the polarizing system.

Accepted Answer

$$I_{\mathrm{trans}} = 1.47\ \mathrm{mW/m}^2$$

Question 17

A bug is placed 10.0 cm in front of a lens. The lens forms an image on a white screen 30.0 cm behind the lens. Which ray diagram correctly shows the formation of the image?

Accepted Answer

Figure a

Question 18

A sodium vapor lamp emits light predominantly at wavelengths of $$589\ \mathrm{nm} ($$yellow-orange) and $$568\ \mathrm{nm} ($$green-yellow). The lamp directs its light onto a diffraction grating with a density of $$400\ \mathrm{lines/mm}. $$This light then projects onto a screen $$2.0\ \mathrm{m}$$ away from the grating. Find the distance between the first-order yellow-orange and green-yellow fringes on the screen.

Accepted Answer

$$6.3\ \mathrm{mm}$$

Question 19

In a controlled experiment, a particle is launched to the left at a velocity of $$0.70c. At $$the same time, a different particle moves to the right at a speed of $$0.50c. $$What is the speed of the first particle, as a fraction of the speed of light ($$c$$), relative to the second particle?

Accepted Answer

$$-0.89c$$

Toroidal Solenoids: Magnetic Field in a Partial Toroid

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