A point charge of 4 μC is placed at the origin. There is an external uniform field E = 400 i N/C. What is the net force on a 5 μC charge placed at (5 m, 3 m)
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To find the net force on a charge in an electric field, you can use the formula:
F = qE
where F is the force, q is the charge, and E is the electric field.
In this case, the charge q is 5 μC (which can be converted to Coulombs by dividing by 10^6), and the electric field E is given as 400 i N/C.
First, let's convert the charge q to Coulombs:
q = 5 μC / 10^6 = 5 x 10^-6 C
Now we can substitute the values into the formula:
F = (5 x 10^-6 C)(400 i N/C)
To multiply a scalar quantity (5 x 10^-6 C) with a vector quantity (400 i N/C), we can distribute the scalar across the vector components:
F = (5 x 10^-6 C)(400 N/C i)
Multiplying these values together:
F = 2 x 10^-3 N i
The net force on the 5 μC charge placed at (5 m, 3 m) can be represented as:
2 x 10^-3 N i