A 23.6μC point charge lies at the origin.
Find the electric field at the point (0.55m , 0). What is the magnitude of the electric field?
Express your answers using two significant figures. Enter the x and y components of the field separated by a comma.
Find the electric field at the point (1.35m , 0.65m ).
Express your answers using two significant figures. Enter the x and y components of the field separated by a comma.
To find the electric field at a point due to a point charge, we can use the formula:
E = k*q/r^2
where:
E is the electric field,
k is the Coulomb's constant (8.99 x 10^9 Nm^2/C^2),
q is the charge, and
r is the distance between the point charge and the point where we want to find the electric field.
Let's use this formula to solve each part of the question.
1. Electric field at (0.55m, 0):
The distance between the origin (where the point charge is located) and (0.55m, 0) is 0.55m. The charge value is given as 23.6µC, which we can convert to Coulombs by dividing by 10^6: q = 23.6 × 10^-6 C.
Now we can substitute these values into the formula:
E = (8.99 × 10^9 Nm^2/C^2) * (23.6 × 10^-6 C) / (0.55m)^2
Calculating this expression will give us the electric field magnitude at (0.55m, 0).
2. Electric field at (1.35m, 0.65m):
The distance between the origin and (1.35m, 0.65m) can be found using the Pythagorean theorem. The distance r is given by:
r = sqrt((1.35m)^2 + (0.65m)^2)
Substituting the values into the formula for r, we get the distance. The charge value is still 23.6µC (converted to Coulombs), and we can use the same formula:
E = (8.99 × 10^9 Nm^2/C^2) * (23.6 × 10^-6 C) / r^2
Calculating this expression will give us the electric field magnitude at (1.35m, 0.65m).
Remember to express both answers using two significant figures and provide the x and y components of the electric field separately.