Electromagnetic Field Theory
A vector field A = p In is given in Cartesian coordinates. In cylindrical coordinates it will be represented as

 A = cosφ Ir + sinφ Iφ.
 A = cosφ Ir.
 A = cosφ Ir - sinφ Ir.
 A = sinφ Ir.

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Electromagnetic Field Theory
Gradient of scalar field is expressed as

 Circulation of a vector field per unit area as the area tends to zero.
 Gradient of divergence of a vector field minus the curl of the vector field.
 Outward flux of a vector field per unit volume as the volume about the point tends to zero.
 Maximum rate of increase of scalar function at a point.

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