Net External Electric Field from Combining Positive & Negative Charges

[colonel]

Suppose there is a positively charged wire inside a negatively charged cylinder. What would be the net external electric field? Would I first need to combine the charges, or can I just combine the separate fields?

 

[Andrew Mason]

Suppose there is a positively charged wire inside a negatively charged cylinder. What would be the net external electric field? Would I first need to combine the charges, or can I just combine the separate fields?

You would draw a Gausian cylinder around the charged cylinder and determine the enclosed charge. Then you would apply Gauss' law to determine the flux through that surface:

[tex]\oint E\cdot dA = \frac{q}{\epsilon_0}[/itex]

where q is the enclosed charge. To find q, just add the charges (negative subtracts from positive). If they sum to 0, there is no external field.

Since E would be the same at all points on the Gausian surface, and since the area of the cylinder is [itex]A = 2\pi RL [/itex] the external field E would be:

[tex]E = \frac{q}{2\pi\epsilon_0RL}[/tex]

AM

 

[thepatientmental]

The net external electric field in this scenario would depend on the distance between the wire and the cylinder, as well as the magnitude of the charges on each object. If the wire and cylinder are close enough, the electric fields from the positive and negative charges would interact and create a combined field. However, if the distance between the objects is significant, then the electric fields would not interact and the net external field would simply be the sum of the individual fields.

To calculate the net external electric field, you would need to combine the charges and calculate the resulting field. This is because the electric field is a vector quantity, meaning it has both magnitude and direction. The individual fields from the positive and negative charges would have different directions, and thus cannot simply be added together as scalar quantities.

In summary, to determine the net external electric field from combining positive and negative charges, you would need to combine the charges and calculate the resulting field. Simply adding the individual fields would not give an accurate representation of the net field.