Week 3

Question 1

In air or water, the electric field causes induced _______ of
(charge separation within) the air or water molecules, which _______ the magnitude of the field by a factor k called the “dielectric constant”

Answer 1

polarization, reduces

Question 2

The field produced by any object (or multiple objects) at any point (x, y) in space can be calculated by ______

Answer 2

dividing it (or them) up into small pieces.
Each is considered a point charge which can have a different net charge

Question 3

• If net charge Q charge is uniformly (evenly) distributed throughout the volume of a sphere, or across only the surface of a sphere, what equation is used to calculate electric field outside the sphere

Answer 3

𝐸 = 𝑘(𝑄/r^2) r^

Question 4

What is 𝑟^ in this equation: 𝐸 = 𝑘(𝑄/r^2) r^

Answer 4

is the unit vector pointing from the center of the sphere to point (x,y)

Question 5

𝐸 = 𝑘(𝑄/r^2) r^: How do you find Q, if the charge per unit volume

Answer 5

Q= q x Volume (sphere volume)

Question 6

In uniformly charged spheres: If Q<0, E ______

Answer 6

points toward the center of the sphere

Question 7

If charge is uniformly distributed along a long,
straight line (e.g., a wire) with charge per unit length what equation is used to calculate magnitude of a field

Answer 7

𝐸 = 2𝑘(|𝜆|/r)

Question 8

In a Uniformly charged line: if line has net positive charge (𝜆 > 0) every point in space points ____

Answer 8

every point in space points away from the line, in a
direction perpendicular to the line

Question 9

In a Uniformly charged line: if line has net positive charge (𝜆 < 0) every point in space points ____

Answer 9

every point in space points toward the line, in a
direction perpendicular to the line

Question 10

DNA has a net negative charge, so a straight
segment of DNA is an example of a ____

Answer 10

a “uniformly charged line”

Question 11

Why in water the field is lower?

Answer 11

E(in water)=E(in empty space)/80.4, since the dielectric constant of water is 80.4

Question 12

How does DNA net charge reduce

Answer 12

Positive ions like Na+ and Mg2+ and Ca2+ are attracted to the negative charged DNA, and bind to it

Question 13

If charge is evenly distributed over a large flat surface with charge per unit area 𝜎 the calculated electric field magnitude is

Answer 13

𝐸 = 2pik|𝜎|

Question 14

In a Uniformly charged large flat surface E is ____ of distance away from the surface!

Answer 14

independent

Question 15

If 𝜎>0 E points

Answer 15

away from the surface (perpendicular)

Question 16

If 𝜎<0 E points toward from the surface (perpendicular)

Answer 16

toward from the surface (perpendicular)

Question 17

With a conductor any net charge (excess protons or electrons) will _____

Answer 17

end up on the surface

Question 18

Cardiologists use measurements of _____ to diagnose diseases

Answer 18

electrical potential (voltage)

Question 19

Pushing +/+ together _____ electric potential energy

Answer 19

increases

Question 20

Conversely, if you have two point charges with opposite signs (+ and –) that attract each other, then pulling them apart requires _________

Answer 20

force and increases potential energy

Question 21

Suppose a point charge q is placed in a uniform electric field with only x-component: Ex=constant. Then q experiences force:

Answer 21

Fx= qEx

Question 22

How to calculate Electric Potential Energy (1D case with uniform field)

Answer 22

−𝑞 𝐸𝑥 (𝑥𝐵- 𝑥𝐴)

Question 23

What is the symbol for Electric Potential Energy

Answer 23

U

Question 24

How to calculate Electric Potential Energy (general 2D case)

Answer 24

deltaU𝐴𝐵 = −𝑞𝐸𝑥(𝑥𝐵− 𝑥𝐴) − 𝑞𝐸𝑦(𝑦𝐵− 𝑦𝐴)

Question 25

To have a single “map” applicable to both + and – charges we introduce a related quantity called

Answer 25

“Electric Potential”

Question 26

Which of the following statements is true about electric potential V? (A) If a positive point charge is moved to a place that has higher V, then U decreases (B) If a negative point charge is moved to a place that has higher V, then U increases (C) Whether or not V increases or decreases when a test charge is moved from one position to another depends on whether the test charge is positive or negative (D) If a test charge is influenced by an electric potential this electric potential must be produced by some other source charges (E) Choose this answer if none of the statements are true

Answer 26

Answer (D): Note that A, B, and C are false since deltaU=q deltaV It is important to remember that a charge that is influenced by an electric potential does not create that electric potential itself, it must be created by other charges in the same manner as an electric field is

Question 27

What is the equation of the magnitude of the field a distance r away (in any direction) from a “source” point charge is

Answer 27

𝐸 = 𝑘(𝑞/𝑟^2)

Question 28

The electric potential produced by this source charge can be determined calculating its difference going from distances rA to rB. What is the equation?

Answer 28

V𝐵 − VA

Question 29

We assume by standard convention that V=0 is a “reference potential” at r=infinity which yields the following expression for potential at any distance r away from a point charge:

Answer 29

V = 𝑘(𝑞/𝑟)

Question 30

electric potential energy equation

Answer 30

deltaUe= qV

Question 31

test point charge will tend to move in a direction that ______ the potential energy Ue of the system

Answer 31

decreases

Question 32

Since deltaV = deltaUe/q this means that a positive test charge will equivalently tend to move towards a place where V is

Answer 32

lower

Question 33

negative test charge q<0 will tend to move towards a place where V is_____

Answer 33

higher (because V = Ue//q implies that V and Ue will have opposite signs in this case)

Question 34

Which of the following statements is NOT true about the electric potential V produced by a point charge? (A) The source charge does not experience electric force due to V (B) The potential produced by a positive point charge increases as you move closer to the point charge (C) The potential produced by a negative point charge decreases as you move closer to the point charge (D) A positive point charge tends to move to a place which increase the potential energy of the system (E) Choose this answer if none of the statements are true

Answer 34

Answer (D): False because both positive and negative point charges tend to move to places which decrease potential energy. That B&C are true can be deduced by looking at the formula that calculates the potential produced by a point charge: V = 𝑘(𝑞/r)

Question 35

We said before that if net charge Q charge is uniformly (evenly) distributed throughout the volume of a sphere, or across only the surface of a sphere, calculations find that the electric field outside the sphere is given by the same formula as for a point charge

Answer 35

𝐸 = 𝑘(𝑄/𝑟^2)𝑟^

Question 36

The electric potential outside such a sphere is also given by the same formula as that for a point charge

Answer 36

𝑉 = 𝑘(𝑄/r)

Question 37

Calculating 𝐸 if you know V

Answer 37

𝐸𝑥 = −𝑑𝑉/𝑑𝑥 and 𝐸𝑦 = −𝑑𝑉/𝑑x

Question 38

It also indicates that Ex and Ey point in the direction of ______ V

Answer 38

decreasing

Question 39

The "power supply" is set in volts to produce a _____ across the gel.

Answer 39

deltaV

Question 40

"Uniform field" means

Answer 40

𝐸=constant in some region of space

Question 41

Since Ex is constant ∆V =

Answer 41

−𝐸𝑥 ∆x