Q: A glass rod is rubbed with a silk cloth and acquires a net charge of $$-3.0\ \mu\mathrm{C}. If $$the initial mass of the rod is $$12\ \mathrm{g}$$, what is the percentage change in its mass due to the charging process? (Assume $$1\ e = 1.6 \times 10$$^{-19}$$\ \mathrm{C}$$ and $$m_e = 9.11 \times 10$$^{-31}$$\ \mathrm{kg}.)$$

$$1.9 \times 10$$^{-13}$$\ \%$$

Q: Two long parallel wires are $$8.0\ \mathrm{cm}$$ apart. Wire 1 carries $$2.20\ \mathrm{A}$$ downward, and wire 2 carries $$3.20\ \mathrm{A}$$ upward. What is the magnitude and nature of the force on a $$0.5\ \mathrm{m}$$ length of one wire due to the other?

(i) $$F = 1.76 \times 10$$^{-5}$$\ \mathrm{N}$$, (ii) The force is attractive

Q: Nano-probes with rest half-life $$3.0\ \mu\mathrm{s}$$ have a half-life of $$6.0\ \mu\mathrm{s}$$ when moving near light speed. Each probe is $$300$$ times as massive as a proton. What is the total energy of a fast-moving nano-probe?

$$6.7 \times 10$$^{-8}$$\ \mathrm{J}$$

Question 1

A glass rod is rubbed with a silk cloth and acquires a net charge of $$-3.0\ \mu\mathrm{C}. If $$the initial mass of the rod is $$12\ \mathrm{g}$$, what is the percentage change in its mass due to the charging process? (Assume $$1\ e = 1.6 	imes 10$$^{-19}$$\ \mathrm{C}$$ and $$m_e = 9.11 	imes 10$$^{-31}$$\ \mathrm{kg}.)$$

Accepted Answer

$$1.9 	imes 10$$^{-13}$$\ \%$$

Question 2

A rectangular surface in the $$xy-$$plane has dimensions $$15.0\ \mathrm{cm} ($$along $$x) $$and $$10.0\ \mathrm{cm} ($$along $$y$$), with its normal in the $$+z$$ direction. An electric field $$\vec{E} = (1500/m) y\ \hat{k}\ \mathrm{N/C} is $$applied. What is the electric flux through the surface?

Accepted Answer

$$2.25\ \mathrm{Nm}^2/\mathrm{C}$$

Question 3

A stationary particle of charge $$+3.25\ \mu\mathrm{C} is at $$the origin. A second particle of charge $$-4.40\ \mu\mathrm{C}$$ moves from $$(-8.50\ \mathrm{cm}, 0) to$$ $$(10.0\ \mathrm{cm}, 12.5\ \mathrm{cm}). $$What is the work done by the electric force on the second particle?

Accepted Answer

$$+0.710\ \mathrm{J}$$

Question 4

For a parallel-plate air capacitor with charge $$Q = 0.200\ \mu\mathrm{C}$$, capacitance $$C = 300\ \mathrm{pF}$$, and plate separation $$d = 0.400\ \mathrm{mm}$$, which of the following is correct for (i) potential difference, (ii) area of each plate, (iii) electric field between plates, and (iv) surface charge density?

Accepted Answer

(i) $$V = 667\ \mathrm{V}$$, (ii) $$A = 0.0136\ \mathrm{m}^2$$, (iii) $$E = 1.67 	imes 10^6$\ \mathrm{V/m}$$, (iv) $$\sigma = 14.8\ \mu\mathrm{C}/\mathrm{m}^2$$

Question 5

Refer to the first circuit diagram provided. What is the power at which electrical energy is converted to other energy forms in the $$6.0\ \mathrm{V}$$ power supply?

Accepted Answer

$$2.91\ \mathrm{W}$$

Question 6

Refer to the second circuit diagram provided. When the $$18.0\ \Omega$$ resistor is removed, the voltmeter reads $$12.0\ \mathrm{V}. $$What is the ammeter reading when the $$18.0\ \Omega is $$replaced with a low resistance shunt?

Accepted Answer

$$1.33\ \mathrm{A}$$

Question 7

A charged particle is observed to curve in its path as it moves through a region. Which observation would best determine if the deflection is due to an existing magnetic field rather than the particle creating a new field?

Accepted Answer

Measurement of the external magnetic field strength.

Question 8

Two long parallel wires are $$8.0\ \mathrm{cm}$$ apart. Wire 1 carries $$2.20\ \mathrm{A}$$ downward, and wire 2 carries $$3.20\ \mathrm{A}$$ upward. What is the magnitude and nature of the force on a $$0.5\ \mathrm{m}$$ length of one wire due to the other?

Accepted Answer

(i) $$F = 1.76 	imes 10$$^{-5}$$\ \mathrm{N}$$, (ii) The force is attractive

Question 9

How does the mutual magnetic force between moving charges illustrate the principles of electromagnetism in practical applications?

Accepted Answer

It enables devices like MRI machines

Question 10

What is magnetic flux?

Accepted Answer

The amount of magnetic field passing through a surface.

Question 11

An LC circuit uses a parallel-plate capacitor with area $$A$$ and inductance $$L. $$The charge oscillates at frequency $$f$$ when the plate separation is $$x$$, with $$x = 4\pi^2$ A \$$epsilon_0$$ f^2$ L. If $$the plate separation changes by $$\Delta x$$ and the frequency changes by $$\Delta f$$, what is the approximate expression for $$\Delta x / x$$?

Accepted Answer

$$2 \frac{\Delta f}{f}$$

Question 12

Refer to the third circuit diagram provided. The current at $$t = 0 is$$ $$I_0. $$For the circuit with $$R_1 = 200$$\ \Omega$$, R_2$ = 300\ \Omega$$, and $$L = 20\ \mathrm{mH}$$, at what time after $$t = 0$$ will the current be $$\frac{1}{4}I_0$?

Accepted Answer

$$55\ \mu\mathrm{s}$$

Question 13

An electric kettle draws $$3.2\ \mathrm{A}$$ from a $$110\ \mathrm{V} AC $$wall socket. What is the current amplitude for the kettle?

Accepted Answer

$$4.5\ \mathrm{A}$$

Question 14

A $$0.20\ \mu\mathrm{F}$$ capacitor is connected to a $$20\ \mathrm{V} AC $$supply at $$200\ \mathrm{kHz}. $$What is the peak current through the capacitor?

Accepted Answer

$$5.0\ \mathrm{A}$$

Question 15

A radio station transmits at $$5.00 	imes 10^6$\ \mathrm{Hz}. $$What is the wavelength and classification of this wave?

Accepted Answer

$$60\ \mathrm{m}$$; Radio wave

Question 16

What is radiation pressure, and why is it significant in the study of electromagnetic waves?

Accepted Answer

Radiation pressure is the force exerted by electromagnetic waves on a surface, significant because it demonstrates the momentum carried by light.

Question 17

An infrared laser emits light into a silicon-based optical fiber (core: $$n = 3.42$$, cladding: $$n = 1.44). $$What is the critical angle for total internal reflection at the silicon-silicon dioxide interface?

Accepted Answer

$$63.4^\circ$$

Question 18

A plano-concave germanium lens (refractive index $$n = 4.01) $$produces an image with magnification $$+0.40$$ from an object $$50\ \mathrm{cm}$$ away. What is the radius of curvature of the curved surface?

Accepted Answer

$$-100\ \mathrm{cm}$$

Question 19

In a double-slit experiment, $$580\ \mathrm{nm}$$ light passes through slits $$0.35\ \mathrm{mm}$$ apart, with a screen $$1.6\ \mathrm{m}$$ away. A thin polythene sheet causes a delay of $$4.5 	imes 10$$^{-16}$$\ \mathrm{s}$$ for one slit. What is this delay as a percentage of the wave's period?

Accepted Answer

$$0.043\%T$$

Question 20

Nano-probes with rest half-life $$3.0\ \mu\mathrm{s}$$ have a half-life of $$6.0\ \mu\mathrm{s}$$ when moving near light speed. Each probe is $$300$$ times as massive as a proton. What is the total energy of a fast-moving nano-probe?

Accepted Answer

$$6.7 	imes 10$$^{-8}$$\ \mathrm{J}$$

Physics Final Exam Study Guidance – Circuits and Magnetism

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