Q: Which equation correctly expresses Gauss's Law for a closed surface?

$$\oint \vec{E} \cdot d\vec{A} = \dfrac{Q_{\text{enclosed}}}{\$$varepsilon_0$$}$$

Q: A $$2\,\mu\text{F}$$ capacitor and a $$4\,\mu\text{F}$$ capacitor are connected in series. What is their total capacitance?

$$C_T = \dfrac{1}{\dfrac{1}{2} + \dfrac{1}{4}} = 1.33\,\mu\text{F}$$

Question 1

A point charge $$Q is $$placed at the origin. What is the electric field at a distance $$r$$ from the charge?

Accepted Answer

$$E = \dfrac{Q}{4\pi\$$varepsilon_0$$ r^2$}$$

Question 2

Which of the following statements about conductors and insulators is correct?

Accepted Answer

In conductors, charges are free to move; in insulators, charges are not free to move.

Question 3

A dipole consists of charges $$+Q$$ and $$-Q$$ separated by distance $$l. $$What is the magnitude of its dipole moment?

Accepted Answer

$$p = Ql$$

Question 4

A particle of mass $$m$$ and charge $$q is $$released from rest in a uniform electric field $$E. $$What is its displacement after time $$t$$?

Accepted Answer

$$x = \dfrac{1}{2} \dfrac{qE}{m} t^2$

Question 5

Which equation correctly expresses Gauss's Law for a closed surface?

Accepted Answer

$$\oint \vec{E} \cdot d\vec{A} = \dfrac{Q_{	ext{enclosed}}}{\$$varepsilon_0$$}$$

Question 6

The electric potential $$V at a $$distance $$r$$ from a point charge $$Q is $$given by:

Accepted Answer

$$V = \dfrac{Q}{4\pi\$$varepsilon_0$$ r}$$

Question 7

A parallel plate capacitor with area $$A$$ and plate separation $$d is $$filled with a dielectric of constant $$K. $$What is the new capacitance?

Accepted Answer

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

Question 8

If a capacitor is disconnected from a battery and a dielectric is inserted, which quantity remains constant?

Accepted Answer

Charge $$Q$$

Question 9

The energy stored in a capacitor is given by which of the following expressions?

Accepted Answer

$$U = \dfrac{1}{2} CV^2$

Question 10

A $$2\,\mu	ext{F}$$ capacitor and a $$4\,\mu	ext{F}$$ capacitor are connected in series. What is their total capacitance?

Accepted Answer

$$C_T = \dfrac{1}{\dfrac{1}{2} + \dfrac{1}{4}} = 1.33\,\mu	ext{F}$$

Question 11

An electron is accelerated through a potential difference of $$100\,	ext{V}. $$What is its energy in electron volts (eV)?

Accepted Answer

$$100\,	ext{eV}$$

Question 12

Which of the following correctly describes the relationship between electric field and electric potential?

Accepted Answer

$$\vec{E} = -
abla V$$

Question 13

A $$5\,\mu	ext{F}$$ and a $$10\,\mu	ext{F}$$ capacitor are connected in parallel. What is their total capacitance?

Accepted Answer

$$C_T = 15\,\mu	ext{F}$$

Question 14

A charged particle moves in a region where the electric field is zero. What happens to its electric potential energy?

Accepted Answer

It remains constant.

Question 15

A parallel plate capacitor has plates of area $$A$$ separated by distance $$d. $$What is the energy density stored in the electric field between the plates?

Accepted Answer

$$u = \dfrac{1}{2} \$$varepsilon_0$$ E^2$

Question 16

A $$3\,\mu	ext{F}$$ capacitor is charged to $$12\,	ext{V}$$ and then disconnected from the battery. If a dielectric with $$K=2 is $$inserted, what is the new voltage across the capacitor?

Accepted Answer

$$6\,	ext{V}$$

Question 17

Which of the following is true for capacitors in series?

Accepted Answer

The charge $$Q on $$each capacitor is the same.

Question 18

A uniform electric field $$E$$ points to the right. A dipole with moment $$p is $$placed in the field at an angle $$	heta to $$the field direction. What is the torque on the dipole?

Accepted Answer

$$	au = pE \sin	heta$$

Question 19

A continuous charge distribution has charge density $$\rho. $$What is the electric field at a point due to a small element $$dQ at $$distance $$r$$?

Accepted Answer

$$dE = \dfrac{1}{4\pi\$$varepsilon_0$$} \dfrac{dQ}{r^2$}$$

Question 20

A parallel plate capacitor is connected to a battery and then a dielectric is inserted. What happens to the charge on the plates?

Accepted Answer

It increases.

Physics with Calculus: Study Notes on Chapters 21–24 (Electricity and Capacitance)

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