Math review

• In packet– Study formulas and chapter summaries– Study “What does it mean to integrate?”

Next two class periods we will do a lot of math review.

The math review test starts next Wednesday

Discussion question: Three charges are placed as shown. Charges A and B are held fixed in place. What direction is the force on C?

A.B.C.D.E. Zero magnitude – no direction

A BC

+q +q -q

Electric Field• The direction of the Electric field is the direction of the

force on a positive point charge at a given point.• Force is a vector• Electric field is a vector

q1 feels a force due to an electric field produced by q2.

21221 ˆ Eqr

r

qkqF

Three charges are placed as shown. Charges A and B are held fixed in place. What direction is the electric field at C?

A.B.C.D.E. Zero magnitude – no direction

A BC

+q +q -q

Can there be an electric field at a point where there is no charge?

●no. A charge must exist in order for an electric charge field to exist.

●Yes an electric field emanates from a charge, therefore at some point where there is no charge there can be a field caused by a nearby charge.

●Yes, There can be an electric field at a point where there is no charge. The electric field is the region of space around a charged object. So all points in this region have the electric field but not necessarily a charge. (although it may)

●Yes, there can be an electric field at a point where there is no charge because similar to the gravitational field, the gravitational field is there regardless of wither or not there is an object there to "feel" that field. The electric field is similar, there does not need to be a charge there to "feel" the field in order for the field to still be there

●I think the first part of the question leaves room for a double meaning. In one sense, it seems to ask: Can an electric field exist without a source charge, in another sense, it sounds like it is asking: if a source charge exists can there be a field without the presence of a test charge? Well, for the former: No, because the charge is what creates the field. If the later: yes, because the test charge just proves the presence of the field, but doesn't create it.

Can there be a charge at a place where there is no field?

• A charge is always in the middle of a field that it creates so wherever there is a charge, at that point there will also be a field.

• There can also be a charge where there is no field because it will feel no force.

• Could I re-word this as, can there be a charge at a place where it feels no electric force?

• Is this the same question?

Discussion question: What direction would the net electric field be at point P at the corner of a square which has an e- at the opposite corner and a proton at the other two corners?

P b +

d c

+ -e

e. The net electric field is zero

a

Discussion question: What direction would the force on an electron be if it is placed at the corner of a square which has an e- at the opposite corner and a proton at the other two corners?

-e b +

d c

+ -e

e. The net force is zero

a

Electric Field

• The direction of the Electric field is the direction of the force on a positive test charge at a given point.

• Radially out of a positive point charge.

• Radially into a negative point charge.

Individual question: A free proton is at a point P in an electric field and experiences a force directed to the right. If the proton is replaced with an electron the electric field at this point

1. Has the same magnitude but changes direction

2. Increases in magnitude and changes direction

3. Remains the same

4. Decreases in magnitude and changes direction.

A charge in an electric field does not affect the electric field that it (the charge) feels.

The electron will feel a force in the opposite direction.

Discussion question: Two charges, +Q and –Q, are located two meters apart and there is a point along the line that is equidistant from the two charges as indicated. Which vector best represents the direction of the electric field at that point?

1. Vector EA

2. Vector EB

3. Vector Ec

4. The electric field at that point is zero.

5. The electric field is opposite to EB

EB

EC EA

+Q -Q

Individual question: Two charges, +Q and +Q, are located two meters apart and there is a point along the line that is equidistant from the two charges as indicated. Which vector best represents the direction of the electric field at that point?

1. Vector EA

2. Vector EB

3. Vector Ec

4. The electric field at that point is zero.

5. The electric field is opposite to EB

EB

EC EA

+Q +Q

Individual question: Two charges, -Q and -Q, are located two meters apart and there is a point along the line that is equidistant from the two charges as indicated. Which vector best represents the direction of the electric field at that point?

1. Vector EA

2. Vector EB

3. Vector Ec

4. The electric field at that point is zero.

5. The electric field is opposite to EB

EB

EC EA

-Q -Q

Work out problem: A charge of +2 C is at the origin. What charge must be placed at 2 m along the positive x axis, to make the electric field at 2 m

along the negative x axis become zero.

1. + 4 C

2. - 4 C

3. + 8 C

4. - 8 C

5. - 2 C

E=0 + 2 C Q

X

2m 2m

rr

kqE ˆ

21

1

What is the Electric field a distance r away from a line of charge?

rr

kqE ˆ

21

1

22 ax

36

12

36

1

ˆn n

n

nntotal r

r

kqEE

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

a

x

rax

kdqEtotal ˆ

22

L

What direction is the E-field?

dq

rxa

kdqE

L

Ltotal ˆ2

222

22

ˆˆˆ

xa

jaixr

dx

dq

L

Q

)ˆˆ(2

2 23

22yaix

xa

dxkE

L

Ltotal

Answers

• 2-b• 4-b• 7-a• 8-c• 11-3• 12-1• 13-2• 14-5• 15-4