Question

A long line carrying a uniform linear charge density+50.0μC/m runs parallel to and 10.0cm from the surface of a large, flat plastic sheet that has a uniform surface charge density of −100μC/m2on one side.Part AFind the location of all points where an α particle would feel no force due to this arrangement of charged objects.L=_____________ m from the line.Part BChoose an appropriate location of these points at a distance calculated in part A.o above the lineo between the line and the sheet.

Answer 1

Answer:

The location of the points is at the distance  above the line charge Option A.

Explanation:

Part A

The electric field due to a line of charge is  expressed as :

Eₐ = λ /2πε₀L  …… (1)

while  the electric field due to a non-conducting elastic sheet is expressed as:

Еₙ =   λ /2ε₀  …… (2)

In order for the  particle to experience no force, the electric field at that point is zero.

Equating  (1) and (2) together, we have:.

λ /2πε₀L = σ /2ε₀  

Rearranging the above expression, we have:

L =  λ /πσ

Substituting 50.0 μC/m  for λ, 3.14 for  π  , and 100 μC/ m² for σ, we have:

L=  50.0 μC/m / (3.14)* 100 μC/ m²

L = 0.159m

From the L value obtained above, the location of all points where an  particle would experience no force due to the arrangement of charged objects is L 0.159m  from the line.

Part B  

The electric field is zero at all the points above the line with the distance 0.159m  from the line.

Thus, the location of the points is at the distance  above the line charge Option A.