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Electric field due to a point charge The electric field in
Chapter 14, Problem 44E(choose chapter or problem)
Electric field due to a point charge The electric field in the xy-plane due to a point charge at (0, 0) is a gradient field with a potential function \(V(x, y)=\frac{k}{\sqrt{x^{2}+y^{2}}}\), where k > 0 is a physical constant.
a. Find the components of the electric field in the x- and y- directions, where \(\mathbf{E}(x, y)=-\nabla V(x, y)\).
b. Show that the vectors of the electric field point in the radial direction (outward from the origin) and the radial component of E can be expressed as \(E_{r}=k / r^{2}\), where \(r=\sqrt{x^{2}+y^{2}}\).
c. Show that the vector field is orthogonal to the equipotential curves at all points in the domain of V.
Questions & Answers
QUESTION:
Electric field due to a point charge The electric field in the xy-plane due to a point charge at (0, 0) is a gradient field with a potential function \(V(x, y)=\frac{k}{\sqrt{x^{2}+y^{2}}}\), where k > 0 is a physical constant.
a. Find the components of the electric field in the x- and y- directions, where \(\mathbf{E}(x, y)=-\nabla V(x, y)\).
b. Show that the vectors of the electric field point in the radial direction (outward from the origin) and the radial component of E can be expressed as \(E_{r}=k / r^{2}\), where \(r=\sqrt{x^{2}+y^{2}}\).
c. Show that the vector field is orthogonal to the equipotential curves at all points in the domain of V.
ANSWER:Solution 44E
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