The infinite sheets in the figure below are both positively charged. The sheet on the left has a uniform surface charge density of 45.4 µC/m2, and the one on the right has a uniform surface charge density of 22.7 µC/m2. (Express your answers in vector form.)
(a) What are the magnitude and direction of the net electric field at points A, B, and C?
EA=N/C
EB=N/C
EC=N/C
(b) What is the force exerted on an electron placed at points A, B, and C?
FA=N
FB=N
FC=N
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This is the 4th or 5th physics question posted, with no sign yet of any thought on your part.
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To find the net electric field at points A, B, and C, we need to consider the electric fields produced by each sheet individually and then add them together vectorially.
Let's start with point A. At this point, the electric field produced by the positively charged sheet on the left will be directed towards the left. To find its magnitude, we can use the formula for the electric field due to a uniformly charged infinite sheet:
E1 = σ1 / (2ε0),
where σ1 is the surface charge density of the left sheet (45.4 µC/m^2) and ε0 is the permittivity of free space. Plugging in the values, we find:
E1 = (45.4 µC/m^2) / (2ε0).
Similarly, the electric field produced by the sheet on the right at point A will be directed towards the right. Its magnitude can be found using the same formula:
E2 = σ2 / (2ε0),
where σ2 is the surface charge density of the right sheet (22.7 µC/m^2). We have:
E2 = (22.7 µC/m^2) / (2ε0).
Note that the direction of the electric field produced by each sheet is perpendicular to the surface of the sheet.
To find the net electric field at point A, we need to subtract the magnitude of the electric field produced by the right sheet from the magnitude of the electric field produced by the left sheet, taking into account their directions. So we have:
EA = E1 - E2 = (45.4 µC/m^2) / (2ε0) - (22.7 µC/m^2) / (2ε0).
The direction of the net electric field at point A will be towards the left if |EA| > |E2| or towards the right if |EA| < |E2|. The magnitude can be calculated using the above equation.
The same procedure can be followed to find the net electric fields at points B and C, by considering the electric fields produced by each sheet individually and then adding them up vectorially.
To find the force exerted on an electron placed at points A, B, and C, we can use the equation:
F = qE,
where q is the charge of the electron and E is the electric field at the respective point. Plugging in the values for the electric field at each point, we can calculate the magnitude of the force.
The direction of the force on the electron will be the same as the direction of the electric field at each point.
Please note that if you want specific numerical answers for parts (a) and (b), you should provide the distance between the sheets or any other necessary information to proceed with the calculations.