Q: At $$r = 15.0\ \mathrm{cm}$$ from the center of the spheres, what is the magnitude of the electric field?

$$\displaystyle \frac{1}{4\pi\$$varepsilon_0$$} \frac{5.00 \times 10$$^{-6}$$}{(0.15)^2$}$$

Q: If the electron in the previous problem is projected with $$v_0 = 2.0$$ \times $$10^7$$\ \mathrm{m/s}$$, what is its velocity as it strikes plate B?

$$\sqrt{(2.0 \times 10^7$)^2 - 2$$ \cdot \frac{eE}{m_e} \cdot d}$

Q: Two small metal spheres, each of mass $$0.0350\ \mathrm{kg}$$, hang from a common point by two thin threads of length $$1.00\ \mathrm{m}. $$Both spheres have the same positive charge and hang with an angle of $$20.0^\circ$$ between them. What is the charge on each ball?

$$\approx 1.2 \times 10$$^{-6}$$\ \mathrm{C}$$

Q: You are given a copper bar of dimensions $$3\ \mathrm{cm} \times 5\ \mathrm{cm} \times 8\ \mathrm{cm}. To $$achieve the smallest possible resistance, you should attach the leads to which pair of opposite faces?

$$5\ \mathrm{cm} \times 8\ \mathrm{cm}$$

Q: For the same copper bar, to achieve the largest possible resistance, you should attach the leads to which pair of opposite faces?

$$3\ \mathrm{cm} \times 5\ \mathrm{cm}$$

Question 1

A solid nonconducting sphere of radius $$R_1 = 10.0$$\ \mathrm{cm}$$ carries a charge of +5.00$$\ \mu\mathrm{C}$$ uniformly distributed over its outer surface. It is surrounded by a conducting shell with inner radius R_2$ = 20.0\ \mathrm{cm}$$ and outer radius $$R_3 = 30.0$$\ \mathrm{cm}$$, carrying a net charge of -8.00$$\ \mu\mathrm{C}$$. What is the total excess charge on the inner surface of the conducting shell?

Accepted Answer

$$-5.00\ \mu\mathrm{C}$$

Question 2

What is the magnitude of the electric field at the center ($$r = 0) of $$the inner sphere described above?

Accepted Answer

$$0$$

Question 3

At $$r = 15.0\ \mathrm{cm}$$ from the center of the spheres, what is the magnitude of the electric field?

Accepted Answer

$$\displaystyle \frac{1}{4\pi\$$varepsilon_0$$} \frac{5.00 	imes 10$$^{-6}$$}{(0.15)^2$}$$

Question 4

A pair of charged conducting plates produces a uniform field of $$E = 12,000\ \mathrm{N/C}$$, directed to the right, between the plates separated by $$40\ \mathrm{mm}. An $$electron is projected from plate A toward plate B with initial velocity $$v_0 = 1.0$$ 	imes $$10^7$$\ \mathrm{m/s}$$. What is the potential difference between the plates?

Accepted Answer

$$480\ \mathrm{V}$$

Question 5

If the electron in the previous problem is projected with $$v_0 = 2.0$$ 	imes $$10^7$$\ \mathrm{m/s}$$, what is its velocity as it strikes plate B?

Accepted Answer

$$\sqrt{(2.0 	imes 10^7$)^2 - 2$$ \cdot \frac{eE}{m_e} \cdot d}$

Question 6

For the capacitive network shown, what is the equivalent capacitance between $$a$$ and $$b$$ when the switch $$S is $$open?

Accepted Answer

$$\approx 13.2\ \mu\mathrm{F}$$

Question 7

For the same network, what is the equivalent capacitance between $$a$$ and $$b$$ when the switch $$S is $$closed?

Accepted Answer

$$\approx 21.0\ \mu\mathrm{F}$$

Question 8

Two capacitors of $$6.00\ \mu\mathrm{F}$$ and $$8.00\ \mu\mathrm{F}$$ are connected in parallel, then in series with a $$14.0\ \mu\mathrm{F}$$ capacitor and a $$12.0\ \mathrm{V}$$ battery. What is the equivalent capacitance of the combination?

Accepted Answer

$$\approx 7.7\ \mu\mathrm{F}$$

Question 9

What is the charge on the $$6.00\ \mu\mathrm{F}$$ capacitor in the above circuit?

Accepted Answer

$$\approx 61.8\ \mu\mathrm{C}$$

Question 10

What is the potential difference across the $$6.00\ \mu\mathrm{F}$$ capacitor in the above circuit?

Accepted Answer

$$7.72\ \mathrm{V}$$

Question 11

Two small metal spheres, each of mass $$0.0350\ \mathrm{kg}$$, hang from a common point by two thin threads of length $$1.00\ \mathrm{m}. $$Both spheres have the same positive charge and hang with an angle of $$20.0^\circ$$ between them. What is the charge on each ball?

Accepted Answer

$$\approx 1.2 	imes 10$$^{-6}$$\ \mathrm{C}$$

Question 12

If a block of neutral metal is placed between the two charged balls described above, what will happen to the balls and the angle between them?

Accepted Answer

The balls will move closer together and the angle will decrease.

Question 13

You are given a copper bar of dimensions $$3\ \mathrm{cm} 	imes 5\ \mathrm{cm} 	imes 8\ \mathrm{cm}. To $$achieve the smallest possible resistance, you should attach the leads to which pair of opposite faces?

Accepted Answer

$$5\ \mathrm{cm} 	imes 8\ \mathrm{cm}$$

Question 14

For the same copper bar, to achieve the largest possible resistance, you should attach the leads to which pair of opposite faces?

Accepted Answer

$$3\ \mathrm{cm} 	imes 5\ \mathrm{cm}$$

Question 15

In a system of three point charges, the charge in the middle is $$Q = -3.1\ \mathrm{nC}. $$For what value of $$q_1$$ will charge $$q_2 be in $$static equilibrium?

Accepted Answer

$$6.2\ \mathrm{nC}$$

Question 16

A parallel-plate capacitor is filled with a dielectric of constant $$K. If $$the area of the plates is $$A$$ and the separation is $$d$$, what is the capacitance?

Accepted Answer

$$C = K \$$varepsilon_0$$ \frac{A}{d}$$

Question 17

A charged ring of radius $$R$$ carries total charge $$Q. $$What is the electric field at a point $$x$$ along the axis of the ring?

Accepted Answer

$$E = \frac{1}{4\pi\$$varepsilon_0$$} \frac{Qx}{(x^2$ + R^2$)^{3/2}$$}$

Step-by-Step Physics Study Guidance for Midterm Exam 1

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