If potential V = 20/(x2 + y2 ). The electric field intensity for V is 40(x i + y j)/(x2 + y2 ) 2 . State True/False.

To determine whether the statement is true or false, we need to find the electric field intensity ( vec{E} ) from the given electric potential ( V ). The electric field is related to the electric potential by the negative gradient of the potential, i.e., ( vec{E} = -nabla V ).

Given the potential ( V = frac{20}{x^2 + y^2} ).

The gradient ( nabla V ) in Cartesian coordinates (with i, j components) is given by:

[ nabla V = frac{partial V}{partial x} hat{i} + frac{partial V}{partial y} hat{j} ]

[ frac{partial V}{partial x} = frac{partial}{partial x} left( frac{20}{x^2 + y^2} right) = -frac{40x}{(x^2 + y^2)^2} ]

[ frac{partial V}{partial y} = frac{partial}{partial y} left( frac{20}{x^2 + y^2} right) = -frac{40y}{(x^2 + y^2)^2} ]

[ nabla V = -frac{40x}{(x^2 + y^2)^2}