Question

 

A point charge of 6.0 x10^-8 C sits on the floor in the middle of a room that is 10 m long. You hold a small cardboard square measuring 1.0 cm x 1.0 cm face down, and carry it across the room at a height of 2.0 m, passing over the position of the point charge. Plot the flux through the square as a function of position, but before doing so, make sure to include the following:

-An explanation of your calculation. Also, show quantitatively that the field at the center of the square is approximately the field at one of the edges.

-A table showing your calculation with the distances, E field, flux values, and other calculations you made.

-Finally, make a plot of the flux as a function of position. Axes must be properly labeled with units.

 

Answer 1

According to Gauss' law,

The size of the cardboard box is very small compared to the size of the room.

The electric field at a distance d is given by

If we take r = 2 m, the smallest value possible,

If we take a distanc eof 0.01 m, which is the length of the cardboard,

This means that we can approximate the cardboard element as a small area element dA with a constant electric field.

So,

Where theta is the angle between the area vector and the electric field.

The height of the cardboard is 2 m.

So,

and

A is the area of the card board = 0.01*0.01 = 10^-4

So, using the values,

We have to change the value of x from -5 to 5.

SInce the length of the room = 10 m and the charge is at th center of the room

So, the table is given below.

x	Flux
-5	0.000692
-4.75	0.000789
-4.5	0.000904
-4.25	0.001042
-4	0.001207
-3.75	0.001407
-3.5	0.001649
-3.25	0.001943
-3	0.002304
-2.75	0.002747
-2.5	0.003291
-2.25	0.003959
-2	0.004773
-1.75	0.005754
-1.5	0.006912
-1.25	0.008232
-1	0.00966
-0.75	0.011082
-0.5	0.012327
-0.25	0.01319
0	0.0135
0.25	0.01319
0.5	0.012327
0.75	0.011082
1	0.00966
1.25	0.008232
1.5	0.006912
1.75	0.005754
2	0.004773
2.25	0.003959
2.5	0.003291
2.75	0.002747
3	0.002304
3.25	0.001943
3.5	0.001649
3.75	0.001407
4	0.001207
4.25	0.001042
4.5	0.000904
4.75	0.000789
5	0.000692

The graph is given below.