Question 1

An alpha particle is accelerated from rest through a potential difference of $$10^6 V. $$What is the final speed of the alpha particle in m/s? (Assume the charge of the alpha particle is $$2e$$ and its mass is $$6.64 	imes 10$$^{-27}$$ kg.)

Accepted Answer

$$3.1 	imes 10^7$

Question 2

A charge of $$1.4 nC is $$uniformly distributed on the surface of a metal sphere with radius $$0.75 m. $$The potential outside, at a point $$0.25 m $$from the center of the sphere is:

Accepted Answer

$$16.8 V$$

Question 3

Three point charges are located on the x-axis: $$q_1 = -q$ at x = 0$, q_2$ = +q at$$ $$x = a$$, and $$q_3 = +q$ at x = 2a$. Calculate the potential energy of the system of three charges.

Accepted Answer

$$-k \frac{q^2$}{2a}$$

Question 4

In the circuit shown, what is the total charge taken from the battery (in $$\muC) $$until the capacitors get fully charged? (Assume all capacitors are $$2 \muF $$and the battery is $$10 V.)$$

Accepted Answer

$$6$$

Question 5

For the previous problem, find the final voltage on capacitor $$C_2.$$

Accepted Answer

$$4 V$$

Question 6

A wire made of a certain material has length $$L$$ and resistance $$R. $$The wire is then stretched to a new length $$4L$$, without losing any mass. Find the new resistance.

Accepted Answer

$$16R$$

Question 7

A circuit consists of a $$12 V $$battery and three resistors: $$R_1 = 2$$ \Omega$$, R_2$ = 4 \Omega$$, and $$R_3 = 3$$ \Omega$$. Find the power (in Watts) supplied by the battery.

Accepted Answer

$$65.5$$

Question 8

Consider a capacitor of capacitance $$C$$ that is being discharged through a resistor of resistance $$R. $$The energy stored in the capacitor decreases with time as the capacitor discharges. After how many time constants is this stored energy one-third its initial value?

Accepted Answer

$$1.098	au$$

Question 9

At room temperature, what is the strength of the electric field in a copper wire (diameter $$2.05 mm) $$that is needed to cause a $$2.45 A $$current to flow? Use the resistivity at room temperature for copper $$ho = 1.72 	imes 10$$^{-8}$$ \Omega \cdot m.$$

Accepted Answer

$$1.28 	imes 10$$^{-2}$$ V/m

Question 10

A parallel-plate capacitor is charged to $$5 V $$and then disconnected. The space between the plates is now filled with a slab of certain dielectric with dielectric constant $$\kappa = 9.6. $$What is the magnitude of the final potential difference across the plates?

Accepted Answer

$$5 V$$

Question 11

For the capacitor network shown in the figure, the potential difference across $$ab is$$ $$220 V. $$Find the total energy stored in this network. ($$35 nF $$and $$75 nF $$capacitors in series)

Accepted Answer

$$0.45 mJ$$

Question 12

What is the potential difference $$V_B - V_A$$ when the $$I = 1.5 A in $$the circuit segment below? ($$20 \Omega$$ and $$12 \Omega$$ resistors in series, $$20 V $$and $$12 V $$batteries as shown)

Accepted Answer

$$+38 V$$

Question 13

A circuit contains three identical resistors in series, and the total current $$I is$$ $$0.20 A. $$What is the value of the resistance $$R of $$the resistors if the total voltage is $$12 V$$?

Accepted Answer

$$30 \Omega$$

Question 14

In the figure below, the battery $$V_1 on $$the right is $$10 V $$and the battery $$V_2 on $$the left is $$20 V. $$The resistances are $$R_1 = 15.0$$ \Omega$$ and R_2$ = 30.0 \Omega. $$Find the current (in amps) through the battery $$V_2.$$

Accepted Answer

$$0.65$$

Question 15

For the circuit shown in the figure, the capacitor is initially uncharged, the connecting leads have no resistance, the battery has no appreciable internal resistance. Determine the time it takes for the capacitor to be charged to $$75\% of $$its capacity. ($$R = 40.0 \Omega$$, $$C = 20.0 \muF)$$

Accepted Answer

$$1.15 	imes 10$$^{-2}$$ s

Question 16

Which of the following integrals is correct for the electric potential in volt (relative to infinity) at the point $$x = +5 on $$the x axis for a line of charge from $$x = -2 to$$ $$x = +3$$?

Accepted Answer

$$\int_{-2}^{3} \frac{k dq}{x-5}$$

Electricity and Magnetism: Key Concepts and Problem-Solving Guide

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