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Electrostatics

Total questions: 69

Worksheet time: 47mins

Name

Class

Date

Guss's theorem of vector calculus connects

volume integral with surface integral

surface integral of divergence of a vector with volm integral of a scalar

surface integral of divergence of a vector with volm integral of the same vector

surface integral of divergence of a vector with volm integral of a different vector

Physical meaning of Guss's law of electrostatics is

Net outward flux through a closed surface is equal to charge enclosed by the volume element

Net inward flux through a closed surface is equal to charge enclosed by the volume element

Net outward flux through a closed surface is equal to charge density enclosed

Net flux through a closed surface is equal to charge density enclosed

Differential form of Guass's law is

div.E=0

div.E=charge density/epsilon-0

div.E=charge/epsilon-0

div.E=charge/epsilon of medium

Electric monopole

can exist as div of E is non zero

can exist as div of E is zero

can not exist as div of E is non zero

can not exist as div of E is zero

D<C<B<A

D>C>B>A

A<B=C<D

C<A=B<D

Total electric flux for the following closed surface which is kept inside water

Less than before

Same as before

More than before

Zero

1=4<2<3

2=4<3<1

2=3<1<4

3<1<2<4

10.

A1 and A2

B1 and B2

Both directions

No stable

11.

A physical quantity has a dimensional formula N/C, it is-

Electrostatic potential energy

Electric flux

Electric field

None of the above

12.

If the electric flux entering and leaving an enclosed

surface respectively is f1 and f2 , the electric charge

inside the surface will be -

(a) (f2 – f1 )x epsilon not

(f2 + f1 ) / epsilon not

(f2 – f1 ) / epsilon not

(f2 + f1 )x epsilon not

13.

When an electric dipole is placed in a uniform electric field, it experiences-

Zero force and zero torque

Non zero force and zero torque

Zero force and non zero torque

Zero force and torque depends on orientation

14.

The electric flux due to any charge depends on

Enclosed Charge by Gaussian surface

Surface area of Gaussian surface

On both - Enclosed Charge by Gaussian surface and Surface area of Gaussian surface

The question is incomplete

15.

An asymmetrically shaped conducting shell is uncharged and contains an isolated point charge +q inside as shown. Which of the following statements is true?

The electric field outside the shell is greatest at the tip of the shell

The electric field just above the surface of the conductor is 0

There electric field between the charge and the shell is 0

The electric potential between the charge and the shell is 0

There are no charges located on the interior of the conductor shell surface

16.

Which of the following labeled points is in the region with the strongest force of electric charge

17.

The sum of the two point charges is 7 micro Coulomb. They repel each other with a force of 1 N when kept 30 cm apart in free space. Calculate the value of each charge?

6 micro coulomb and 1 micro coulomb

5 micro coulomb and 2 micro coulomb

3 micro coulomb and 4 micro coulomb

4.5 micro coulomb and 2.5 micro coulomb

18.

An electric dipole of dipole moment 20*10^-6 Cm is enclosed by a closed surface. What is the net flux coming out of the surface?

19.

Which of the physical quantities has the unit N/C? It is a vector or scalar quantity ?

Electric Field, vector

Electric potential,Scalar

Electric Field,Scalar

Electric potential,Vector

20.

What is the amount of work done in moving a 100 nC charge between two point 5cm apart on an equipotential surface?

don't know

21.

Which physical quantity has unit Joule per Coulomb is it a vector or scalar quantity?

potential difference,vector

Electric field, vector

potential difference,scalar

Electric field,scalar

22.

What orientation of an electric dipole in a uniform electric field corresponds to its stable equilibrium?

30 degree

perpendicular

dipole moment along the direction of the electric field then it will be in stable equilibrium.

parallel

23.

A metal sphere with radius r1 has a total electric charge of magnitude q. An uncharged metal sphere with radius r2 (with r1 > r2) is then connected by a wire to the first sphere, as illustrated above. The separation of the spheres is much greater than the radius of either sphere. When equilibrium is reached, the spheres will have

charges on their surfaces of equal magnitude and the same sign

charges on their surfaces of equal magnitude and opposite sign

equal electric fields at their surfaces

equal capacitances

equal electric potentials

24.

A positive electric charge is moved at a constant speed between two locations in an electric field, with no work done by or against the field at any time during the motion. This situation can occur only if the

charge is moved in the direction of the field

charge is moved opposite to the direction of the field

charge is moved perpendicular to an equipotential line

charge is moved along an equipotential line

electric field is uniform

25.

A proton moving along the positive x-axis enters an electric field that is directed along the positive y-axis. What is the direction of the electric force acting on the proton after it enters the electric field?

along the negative z-axis

along the positive z-axis

along the negative y-axis

along the positive y-axis

The direction cannot be determined since the magnitude of the electric field is not known

26.

A capacitor is constructed of two identical conducting plates parallel to each other and separated by a distance d. The capacitor is charged to a potential difference of V0 by a battery, which is then disconnected.

A sheet of insulating plastic material is inserted between the plates without otherwise disturbing the system. What effect does this have on the capacitance?

It causes the capacitance to increase

It causes the capacitance to decrease

None; the capacitance does not change

Nothing can be said about the effect without knowing the dielectric constant of the plastic

Nothing can be said about the effect without knowing the thickness of the sheet.

27.

Two small spheres are arranged along a line and carry charges of +4Q and –3Q, as shown in the figure above. The vertical lines are equally spaced.

At which of the labeled points does the electric field point toward the right with the smallest magnitude?

28.

A charge +𝑄 is inside a hollow region in an electrically neutral piece of solid metal, as shown above. The dashed line represents a Gaussian surface within the metal that completely encloses the hollow region.

At which of the three labeled points is the electric field equal to zero?

X only

Y only

X and Z only

Y and Z only

X, Y, and Z

29.

The conducting sphere in Figure 1 has a charge of −Q

and is electrically isolated so that there is no conducting path to or from the conducting object shown in Figure 2. The charges on the sphere are in equilibrium. The same charge −Q

is on the isolated conducting object. Which of the following correctly describes a change between the sphere in Figure 1 and the object in Figure 2?

The charge is no longer located entirely on the surface of the object.

The electric field inside the object is no longer zero everywhere

The electric potential is no longer the same at all points inside the object.

The electric field is no longer directed perpendicular to the surface at all points on the object

The magnitude of the electric field is no longer the same at all points on the surface

30.

If the only force acting on an electron is due to a uniform electric field, the electron moves with constant

acceleration in a direction opposite to that of the field

acceleration in the direction of the field

acceleration in a direction perpendicular to that of the field

speed in a direction opposite to that of the field

speed in the direction of the field

31.

A battery or batteries connected to two parallel plates produce the equipotential lines between the plates shown above.

The force on an electron located on the 0-volt potential line is

0 N

1 N, directed to the right

1 N, directed to the left

directed to the right, but its magnitude cannot be determined without knowing the the distance between the lines

directed to the left, but its magnitude cannot be determined without knowing the distance between the lines

32.

A battery or batteries connected to two parallel plates produce the equipotential lines between the plates shown above.

The force on an electron located on the 0-volt potential line is

Q₂ = 16Q₁

Q₂ = 4Q₁

Q₂ = Q₁

Q₂ = 0.25Q₁

33.

The above circuit is designed with an ideal battery and a capacitor. When the capacitor is fully charged, the charge on the capacitor plates has a magnitude Q. Which of the following is a correct hypothesis for what will happen to the capacitor when a material of dielectric constant κ is inserted between the capacitor plates?

The charge stored on the capacitor will increase

The charge stored on the capacitor will decrease

The potential difference across the plates of the capacitor will increase

The potential difference across the plate of the capacitor will decrease

The energy stored on the capacitor will remain the same

34.

A capacitor with unknown capacitance is used for an experiment. Students connect the capacitor to a battery, allow the capacitor to become fully charged, and then isolate the capacitor. The students then insert dielectrics with different dielectric constants κ, one at a time, between the plates of the capacitor and measure the potential difference V across the capacitor. Which of the following hypotheses can be tested with this data?

For a given the potential difference V, the charge stored in a capacitor will increase as the dielectric constant of the material between the plates increases.

For a given the potential difference V, the energy stored in a capacitor will increase as the dielectric constant of the material between the plates increases.

For a given the potential difference V, the charge stored in a capacitor will increase as the capacitance of the capacitor increases.

For a given stored charge, the breakdown voltage of a capacitor will decrease as the dielectric constant of the material between the plates increases.

For a given stored charge, the potential difference across the plates of a capacitor will increase as the dielectric constant of the material between the plates increases.

35.

If a dielectric is inserted between the plates of a capacitor while the capacitor maintains its connection to a constant voltage source, which of the following is true?

The capacitance of the capacitor is unchanged

The charge on the capacitor plates increases

The potential difference across the capacitor increases

The electric field between the capacitor plates increases

The electric field between the capacitor plates decreases

36.

A hollow conducting sphere is surrounded by a larger concentric spherical conducting shell, as shown above. The inner sphere has a net charge of –Q, and the outer sphere has a net charge of +3Q.

What is the net charge on the outer surface of the spherical shell?

+2Q

+3Q

+4Q

37.

A solid, conducting sphere with zero net charge is placed into a uniform electric field. Which of the following happens immediately after the sphere is placed in the field?

An electric field is momentarily set up on the conducting sphere, redistributing the charges until the surface again becomes equipotential.

A nonuniform electric field is permanently set up inside the conducting sphere, pushing charges to the surface of the sphere.

The external electric field redistributes the charges evenly inside the sphere, resulting in the electric field becoming zero inside the sphere.

The electric field aligns the charges inside the sphere in such a way that they create a uniform electric field inside the sphere that is equivalent to the external electric field.

The electric field does not interact with the sphere since it has zero net charge.

38.

When two metal objects, X and Y, are connected to each other by a conducting wire, object X gains electrons. From this information, it can be inferred that before the connection was made, object X, compared with object Y, must have had

less capacitance

more electrical potential energy

a smaller dielectric constant

a greater electric charge

a greater electric potential

39.

A uniform electric field exists in which of the following regions?

I. Around an infinite line of uniform linear charge density

II. On either side of an infinite thin sheet of uniform charge density

III. Between the spherical shells of a charged spherical capacitor

I only

II only

III only

II and III only

I, II, and III

40.

The figure above shows an object in the shape of an arc. The object has a uniform charge distribution. The three labeled vectors show possible directions of the electric field at point P

at the center of the arc. Which of the following options indicates the vector that shows the correct direction of the electric field and provides a correct physical explanation for this direction?

Vector A: the charge distribution is positive, and there are more charges to the left of point P

Vector A: the charge distribution is negative, and there are more charges to the left of point P

Vector B: the charge distribution is positive, and there are more charges above point P

Vector B: the charge distribution is negative, and there are more charges above point P

Vector C: the charge distribution is positive, and there are no charges below and to the left of point P

to cancel the field from charges above and to the right of point P

41.

Which of the following must be true for a Gaussian surface through which the net flux is zero?

I. There are no charges inside the surface.

II. The net charge enclosed by the surface is zero.

III. The electric field is zero everywhere on the surface.

I only

II only

III only

I and II only

I, II, and III

42.

The graph above shows the electric field E as a function of x, where x is the distance from a given charge arrangement in an xyz-coordinate system. Which of the following could be the arrangement?

A positive point charge at x = 0

Positive charges uniformly distributed inside a sphere with x = 0 on the sphere’s surface

Positive charges uniformly distributed on the surface of a sphere with x = 0 on the sphere’s surface

Positive charges uniformly distributed along the y-axis

Positive charges uniformly distributed over the yz-plane

43.

44.

Four charges are placed at the corners of a square of sides 2a as shown above. What is the magnitude and direction of the electric field at the origin?

$\frac{kq\sqrt{2}}{a^2}\ left$

$\frac{kq\sqrt{2}}{a^2}\ right$

$\frac{4kq\sqrt{2}}{a^2}\ left$

$\frac{4kq\sqrt{2}}{a^2}\ right$

$\frac{kq\sqrt{2}}{4a^2}\ right$

45.

Four charges are placed at the corners of a square of sides 2a as shown above. What is the electric potential at the origin?

zero

$\frac{kq}{\sqrt{2}}$

$\frac{4kq}{\sqrt{2}}$

$\frac{-kq}{\sqrt{2}}$

$\frac{-4kq}{\sqrt{2}}$

46.

An electron is released in an area of space occupied by an electric field. Which of the following statements is true?

The electron will move from high to low potential

The electron will feel a force in the direction of the electric field

The electron will move parallel to the equipotential lines

The field will do work on the electron

The electron will accelerate at a rate directly proportional to its mass

47.

48.

An insulator plate is rubbed with a cloth to give it a charge. A conducting plate, attached to an insulating handle, is then placed on top to the insulator and briefly grounded by touching it. The conductor is held by the handle and lifted from the insulator plate. Which of the following is true?

After grounding, the insulator plate is no longer charged

After grounding, the conductor has no charge

The cloth used to rub the insulator plate has no charge

The cloth and the conducting plate will be attracted to each other

The cloth and the conducting plate will be repelled by each other

49.

50.

51.

A proton is traveling to the left when in enters the space between two charged plates as shown. Which path will the proton take?

52.

+ + +

+ 0 0

0 0 +

0 + +

53.

$F_A=F_C>F_B$

$F_B>F_C=F_A$

$F_A=F_B>F_C$

$F_A>F_C>F_B$

54.

Two pieces of neutral tape are stuck together. The sticky side of the top piece is stuck to the back of the bottom piece and then pulled apart quickly. Afterward, the nonsticky sides of both are brought near each other and they attract. This is evidence that:

The two pieces of tape have equal amounts of excess charge

The are two types of charge, and these two attract each other

The charge on the top piece is negative and the charge on the bottom is positive

The charge on the pieces is due to electrons moving from one piece to the other

55.

Four charges are arranged as shown. A proton is brought from very far away and placed at each of the points, A, B, and C. Rank the energy required to move the proton from very far away to each of these points.

$A>B>C$

$B>C>A$

$C>A>B$

$C>B>A$

56.

Where is the electric field stronger?

57.

Which point is at a lower electric potential?

58.

A solid non-conducting sphere has a radius R and a charge of +Q uniformly distributed throughout its volume. Which graph below describes the electric field as a function of distance r from the center of the sphere?

59.

A spherical conductor is given a positive charge. Under electrostatic conditions, which of the following is TRUE of the electric field just beneath the surface of the sphere?

The electric field is directed away from the center of the sphere.

The electric field in infinitely large.

The electric field is zero.

The electric field depends on the radius of the sphere.

The electric field is directed tangential to the surface of the sphere.

60.

A billion electrons are added to a body, its charge becomes

1.6 X 10^-19 C

1.6 X 10^-28 C

-1.6 X 10^-10 C

-1.6 X 10^-28 C

61.

Which graph best represents the relationship between the strength of an electric field and distance from a point charge?

62.

As a proton moves in the direction the electric field lines...

it is moving from low potential to high potential and gaining electric potential energy.

it is moving from low potential to high potential and losing electric potential energy.

it is moving from high potential to low potential and gaining electric potential energy.

it is moving from high potential to low potential and losing electric potential energy.

63.

In a region where the electric field is uniform and points in the +x direction, the electric potential is -2000 V at x = 8 m and is +400 V at x = 2 m. What is the magnitude of the electric field?

500 V/m

600 V/m

200 V/m

400 V/m

64.

The S.I. unit of electric flux is

Joule per coulomb

Newton per coulomb

Weber

Volt metre

65.

If the electric flux entering and leaving an enclosed surface respectively is $\phi_1$ and $\phi_2$ the electric charge inside the surface will be

$\left(\phi_1+\phi_2\right)\in_0$

$\left(\phi_1-\phi_2\right)\in_0$

$\frac{\left(\phi_1+\phi_2\right)}{\in_0}$

$\frac{\left(\phi_1-\phi_2\right)}{\in_0}$

66.

A conducting sphere has a charge +Q and a radius R. Which graph below describes the electric field as a function of distance r from the center of the sphere?

67.

The area vector for a flat surface

is parallel to the surface and has a magnitude equal to the length of a side of the surface.

is perpendicular to the surface and has a magnitude equal to the length of a side of the surface.

is parallel to the surface and has a magnitude equal to the area of the surface.

is perpendicular to the surface and has a magnitude equal to the area of the surface.

68.

The flux of the electric field (24 N/C)i + (30 N/C)j + (16 N/C)k through a 2.0 m² portion of the yz plane is:

32 N × m²/C

34 N × m²/C

42 N × m²/C

48 N × m²/C

69.

A charge -2Q is placed at A ( 3,0,0) cm and another charge 8Q is placed at B ( 1,0,0)cm. Find the ratio of electric flux through concentric spheres S₁ and S₂centered at the origin with radius 2 cm & 5 cm respectively

4/3

1/4

4/5

1/8

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Electrostatics

Total questions: 69

Worksheet time: 47mins

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