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Solved Problem on Electric Field
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A point charge 10 nC is located in an electric field. The field exerts a force of 1×10−2 N, horizontally and from left to right, find:
a) The magnitude and direction of the electric field;
b) If the charge were replaced by a charge of −2 µC, what would be the magnitude and direction of the new force acting on the charge?


Problem data
  • electric charge:    q = 10 nC = 10×10−9 C;
  • electrical force:    F = 1×10−2 N.
Solution

a) Since the charge is positive, the vectors representing the electric force and the electric field are in the same direction (figure 1).
The magnitude of the electric force and the magnitude of the electric field are related by the expression
\[ \bbox[#99CCFF,10px] {F=qE} \]

Electric charge q in an electric field E and electric force F acting on the charge.
figure 1
so the magnitude of the electric field can be written as
\[ E=\frac{1 \times 10^{-2}}{10 \times 10^{-9}}\\ E=\frac{1 \times 10^{-2}}{1 \times 10^{-8}}\\ E=1 \times 10^{-2} \times 1 \times 10^{8}\\ E=1 \times 10^{6}\;\text{N/C} \]
The electric field will be (figure 1)

magnitude:  1 × 106 N/C;
direction:  horizontal pointing to right as the electric field.

b) For a charge of −2×10−6 C, we have an electric force of magnitude
\[ F=qE\\ F=-2 \times 10^{\;-6} \times 1 \times 10^{6}\\ F=-2\;\text{N} \]

Electric charge q immersed in an electric field E under the force F.
figure 2
The electric force will be (figure 2)

magnitude:  − 2 N;
direction:  horizontal pointing to left, opposite to the electric field.


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