curl

Given F = a_x(3y + k_1z) + a_y(k_2x - 2z) + a_z(k_3y – x), where a_x, a_y and a_z are the unit vectors in Cartesian coordinate system. The product k_1k_2k_3 for which F is irrotati...

If the magnetic field intensity ($$\overrightarrow H $$) in a conducting region is given by the expression, $$\overrightarrow H = {x^2}\widehat i + {x^2}{y^2}\widehat j + {x^2}{y^2...

The figures show diagramatic representations of vector fields $\vec{X}$, $\vec{Y}$, and $\vec{Z}$, respectively. Which one of the following choices is true?

In cylindrical coordinate system, the potential produced by a uniform ring charge is given $$\phi=f\left(r,\;z\right)$$, where f is a continuous function of r and z. Let $$\overrig...

The curl of the gradient of the scalar field defined by $$\,V = 2{x^2}y + 3{y^2}z + 4{z^2}x$$ is

In electrostatic field $$\nabla\times\overrightarrow E\equiv0$$