Consultation Hours @ A101:

T 10-11am, 3-4pm

ThF 10am-12nn, 2:15-4:15pm

Attendance Quiz: Sec 21-5

Find the magnitude and direction of the net electric

field at the location of charge A. Express your answer in terms of , 0 , , .

Electric Field Calculations

Objective

Evaluate the electric field at a point in space due to a system of arbitrary charge distributions

Notations:

Point charge (q)

Linear charge density () Charge per unit length

Area charge density () Charge per unit area

Volume charge density () Charge per unit volume

Approach: Discrete charge distribution

1. Make a sketch for the problem, clearly showing the chosen coordinate axes, charge locations, and field point location. Identify and indicate all needed information.

2. Obtain the electric field contribution one by one. Write the electric field vector in component form.

3. Magnitude is obtained using Coulombs law.

4. NET electric field vector obtained using superposition principle.

Attendance Quiz: Sec 21-5

Find the magnitude and direction of the net electric

field at the location of charge A. Express your answer in terms of , 0 , , .

Example 1: Ring of Charge

Charge q is uniformly distributed around a conducting ring of radius a. What is the electric field at point P on the ring axis at a distance x from its center?

Approach: Continuous charge distribution

1. Make a sketch for the problem, clearly showing the chosen coordinate axes, charge locations, and field point location. Identify and indicate all needed information.

2. Define a small charge element, find its electric field. Write electric field vector in component form.

3. Integrate to get total field of all charge elements.

Example 1: Ring of Charge

Charge q is uniformly distributed around a conducting ring of radius a. What is the electric field at point P on the ring axis at a distance x from its center?

Magnitude:

Direction: along positive x-axis

Example 2: Uniformly charged disk

A nonconducting disk of radius R has a uniform positive surface charge density . What is the electric field at a point along the axis of the disk a distance x from its center? Assume that x is positive.

Approach: Continuous charge distribution

1. Make a sketch for the problem, clearly showing the chosen coordinate axes, charge locations, and field point location. Identify and indicate all needed information.

2. Define a small charge element, find its electric field. Write electric field vector in component form.

3. Integrate to get total field of all charge elements.

Example 2: Uniformly charged disk

A nonconducting disk of radius R has a uniform positive surface charge density . What is the electric field at a point along the axis of the disk a distance x from its center? Assume that x is positive.

Magnitude:

Direction: along positive x-axis

Example 3: Infinite plane sheet

In the limit that the nonconducting disk in Example 2 is very large or that field point is very close it such that R>>x, we get

Magnitude:

Direction: everywhere perpendicular to sheet, away from it.

Example 4: Two oppositely charged infinite sheets

Two infinite plane sheets with uniform charge densities + and are placed parallel to each other with separation d. What is the electric field above the upper sheet, below the lower sheet and between the sheets?

Attendance Quiz: Line charge

Positive charge Q is distributed uniformly along the y-axis between y= and y= +. What is the electric field at point P on the x-axis a distance x from the origin?

Attendance Quiz

Answer the following:

(a) What is the linear charge density , in terms of Q and a?

(b) Define a small charge element by considering a small segment of length d. What is the charge d of this segment, in terms of Q and a?

(c) What is the electric field at point P due to this segment? Write the field vector in component form.

(d) What is the integral expression that gives the total electric field due to the whole line charge?

Line charge Positive charge Q is distributed uniformly along the y-axis between y=-a and y=+a. What is the electric field at point P on the x-axis a distance x from the origin?

Magnitude:

Direction: along positive x-axis if > 0, along negative x-axis is < 0.

Electric Field (line charge)

Very long segment or field point very close to it such that a>>x, the square root term becomes negligible.

Electric Field (Infinite line charge)

02lineE

R

At any point P at a perpendicular distance x=R

Objective

Evaluate the electric field at a point in space due to a system of arbitrary charge distributions

End.

Attendance Quiz Coverage for Wednesday, January 28:

21-6 Electric Field Lines and

21-7 Electric Dipoles

Lecture outline:

1) Efield calculations index card exercises

2) Sec 21-6 Electric Field Lines

3) Sec 21-7 Electric Dipoles