Concept explainers
The magnitude of the electric field at the given position.
Answer to Problem 49P
The magnitude of the electric field at the given position is
Explanation of Solution
The coulomb constant is
The given figure below shows the electric field due to two charges at the given point.
Write the expression for
Here,
Write the expression for
Write the expression to calculate the electric field along x direction due to two charges.
Here,
Rewrite the above equation using the expression for
Here, x is the horizontal distance from the charge to the point.
Write the expression to calculate the electric field along y-direction.
Here,
Rewrite the above equation using the expression for
Here, y is the vertical distance from the charges to the point.
Write the expression to calculate the net electric field due to both charges.
Here, E is the net electric field due the two charges.
Rewrite the above equation using (I) and (II).
Write the expression to calculate r.
Rewrite the equation for E using the above expression.
Substitute
Conclusion:
Therefore, the magnitude of the electric field at the given position is
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