Description

Charges and Fields

Electric Field due to a Point Charge

Concept: the electric field due to a point charge is given by

βπ¬

β = π²ππ π

Μπ

π

An electric field can be visualized on paper by drawing lines of force, which give an

indication of both the size and the strength of the field. Lines of force are also called

field lines. Field lines start on positive charges and end on negative charges

Procedure

Go to the web site

Once you are at the site βcharges and fieldsβ Click βplayβ.

The simulation contain the following items

A positive charge particle of 1 nC = 10-9 C

A negative charge particle of 1 nC = 10-9 C

A sensor that shows the value of the Electric Field at any point in space in V/m

A distance measuring tape in cm.

A grid that shows the direction of the electric field.

I.

Measurement of magnitude and direction of the Electric field due to

a point charge

The electric field for a point charge is given by

βπ¬

β = π²ππ π

Μπ

π

——— (*)

Where the constant k is given by K = 8.99 x 109 Nm2/C2

For the simulation q = 10-9 C. The magnitude of the electric field is going to be measured at

different directions and different distance r from the point charge. Note that the sensor in

the simulation gives the value of E in Volt/meter (V/m). It can be shown that 1 V/m= 1 N/C.

Notice the scale of 1 m in the grid in the lower left corner.

π²π

Μπ as E1, actually is an

Letβs denote the value for E obtained by the equation βπ¬ = ππ π

experimental value because you need to measure r. Denote the value obtained by the sensor

as E2. Then calculate the % difference using the formula below

Note:

Percent difference is practically the same as percent error, only instead of one

βtrueβ value and one βexperimentalβ value, you compare two experimental

values. The formula is:

——–( **)

Procedure

1. Measure the Electric Field of the point charge in a direction of 0Β°

Move the positive point charge to the center of the plane. Assume this position as the

origin.

Click in the boxes in the upper right side to activate the electric field direction,

voltage, values, grid.

Use the sensor (yellow circle) to measure the Electric field at different points along

the x axis. The sensor gives the value of the electric filed in V/m

Complete the table below

X (m)

Distance from

the positive test

charge

E2 using the

sensor V/m

|π¬π |

% error from

from equation (*) equation (**)

in N/m

0.5

1

1.5

2.0

2.5

3.0

3.5

4.0

2. Measure the Electric Field of the point charge in a direction of 90Β° with respect to

+x direction

Y (m)

Measured

vertically from

the positive

charge

0.5

1

1.5

2.0

E2 using the

sensor (V/m)

|π¬π |

% error from

from equation (*) equation (**)

in N/m

3. Measure the Electric Field of the point charge in a direction of 45Β° with respect to +

x direction.

Use the measuring tape to verify the value of r. At 45Β°, follow the diagonal of the

square grid

r (m)

E2 using the

sensor V/m

|π¬π |

from equation

(*) in N/m

% error from

equation (**)

0.705

1.41

2.12

2.82

4. Measure the Electric Field of the point charge in a direction of 45Β° with the negative

x direction

Use the measuring tape to verify the value of r. At 45Β°, follow the diagonal of the

square grid

r (m)

0.705

1.41

2.12

2.82

E2 using the

sensor V/m

|π¬π |

from equation

(*) in N/m

% error from

equation (**)

Analysis

Do Excel plots

Plot E2 vs distance x. You have to make two plots, one for the results of part 1

and one for part 2. The plots must be a scatter plot. Do not joint the points

with a curve. Below is an example of the Excel plot

E from the sensor (N/m) vs x (m). Data of part 1

45

40

35

30

25

20

15

10

5

0

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Questions

1. Do you obtain the same values for the electric field at directions of 0Β° and 90Β° for

the same distance?

2. Do you obtain the same value of the electric field for symmetric points at a

direction of 45Β° with positive x and at a direction of 45Β° with negative x?

3. Verify that the magnitude of the electric filed must be the same at points at the

same distance from the charge. From your data from part 1 and 2 complete the

table below

Use data from part 1 and part 2 to complete the table

X (m)

E2 using the

sensor (V/m)

from part 1

Y (m)

0.5

0.5

1

1

1.5

1.5

2.0

2.0

4. Write conclusions

E2 using the

sensor (V/m)

From part 2

% error

difference

using E2 for

the X and E2

for the Y

direction

from equation

(**)

II.

Electric Field due to two point charges.

To find the electric filed of two point charges at a given point in space, apply the principle of

superposition.

βπ¬

β πππππ = βπ¬π + βπ¬π ;

——(***)

At a given distance r; E total is given by

βπ¬

β πππππ =

π²ππ

ππ

Μπ +

π

π²ππ

ππ

Μπ ——–(***)

π

In the simulation the numerical values of q1 equal q2 are equal, and keep in mind that q2 is

negative

Procedure:

Locate both charges positive and negative separated a distance of 4 m. Assume the origin is

located at the position of the positive charge and place the positive charge to the left of the

negative charge

Calculate the coulomb force for a distance of 4 m

|ππππππππ| =

π²ππππ

ππ

=

_______________ N

Find the total electric field of the two point charges along the axis that connects the

charges. Remember the origin is located at the positive charge, and positive x is the

direction to the right of the positive charge. Denote q1, r1 for the positive charge and q2 and

r2 for the negative charge

Complete the table:

r1 (m)

1

2

3

5

6

7

-1

-2

E1 (N/C)

From

equation

(*)

Direction

of E1

+X or -X

.r2 (m)

E2 (N/C)

From

equation

(*)

Direction

of E2

+X or -X

E total

from

equation

***

(N/C)

Direction

+X or -X

Complete the table using the sensor

.r1 (m)

Etotal using the

sensor in V/m

Direction +X or

-X

Etotal from the

previous table

(N/C)

% error

difference from

equation (**)

1

2

3

5

6

7

-1

-2

———(**)

Question

1. The % error difference increase, decrease or is random as function of

distance r.

2. Show that 1 V/m is equal to 1 N/C. Use the concept that 1 V = 1 Joule/C

3. Conclusions.

Series and Parallel circuits Lab

Name:

Series circuit

+

–

Parallel

+

–

Arrange bulbs in series and parallel circuits. Include pictures of each set-up.

In which set-up are the bulbs brighter?

Try is for both series and parallel, if one bulb is removed will the other go out?

Extra credit: If you have two batteries, can the batteries be arranged in series and parallel.

Which is brighter? Explain why this is.

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