Question

In: Physics

A point charge of 6.0 x10-8 C sits on the floor in the middle of a room that is 10 m long.

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.

Expert Solution

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.

genius_generous answered 2 years ago

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