Because Electric field can be expressed as the gradient of a scalar. Curl of a gradient is always zero by rules of vector calculus.
Curl represents the force of rotation in a 3-D vector field. Generally, the curl vector at a given point is the answer to the question, "What would happen if I stuck something there that could spin but couldn't move?" Unless the curl is zero, it would spin perpendicularly to the curl vector (according to the right-hand rule), and the longer the vector is, the faster. Curl is mathematically defined in a given direction as the limit of "circulation over area", i.e. the line integral of a circle around the point, divided by the area of the circle, with the circle shrinking towards the point. More practically, the actual vector can found by taking the cross product of the gradient operator with the function that defines the field: curl_x = ∂F/∂y - ∂F/∂z curl_y = ∂F/∂z - ∂F/∂x curl_z = ∂F/∂x - ∂F/∂y
In mathematics, the curl of a vector is the maximum rotation on a vector field, oriented perpendicularly to the certain plane. The curl of a vector is defined by this form: ∇ x F = [i . . . . j . . . . . k] [∂/∂x ∂/∂y ∂/∂z] [P. . . Q. . . .R. . ] ...given that F = <P,Q,R> or Pi + Qj + Rk Perform the cross-product of the terms to obtain: ∇ x F = (∂R/∂y - ∂Q/∂z)i + (∂P/∂z - ∂R/∂x)j + (∂Q/∂x - ∂P/∂y)k
Curl is the rotation of wind field
The vorticity vector is DelxV = v/r sin(RV)H1, the Curl of the vector V. The unit vector H1, is perpendicular to the plane formed by the radius vector R and and the vector V.
The velocity at each point in the fluid is a vector. If the fluid is compressible, the divergence of the velocity vector is nonzero in general. In a vortex the curl is nonzero.
Yes. For any vector field, force included, to be conservative, it must be irrotational, meaning that its curl must be zero everywhere. Fortunately (for me at least, since it makes this answer a whole heck of a lot easier to explain), the magnetic force field vector is already commonly expressed as a curl via Maxwell's equations:Ã¢Ë†â€¡ X B = ÃŽÂ¼0J + ÃŽÂ¼0ÃŽÂµ0Ã¢Ë†â€šE/Ã¢Ë†â€št,where B is the magnetic field, ÃŽÂ¼0 is the permeability of free space, ÃŽÂµ0 is the permittivity of free space, J is the current density, E is the electric field, t is time, and Ã¢Ë†â€¡ X B is the curl of the magnetic field. Bolded quantities are vectors.Now, if you don't know a thing about vector calculus, hopefully you at least remembered what I wrote above. For a vector field to be conservative, its curl must be zero everywhere. As you can hopefully see from that above equation, the curl of the magnetic field, Ã¢Ë†â€¡ X B, is not zero everywhere. More specifically, if there is a current density, J, within the magnetic field, or if there is a time changing electric field, Ã¢Ë†â€šE/Ã¢Ë†â€št, within the magnetic field, the curl of the magnetic field is not zero, therefore the magnetic force field is nonconservative.If you get lucky enough to find a situation where there is no current density or time dependent electric field, which is in reality impossible due to electrons providing there own time dependent electric fields, then the magnetic force field would be conservative.
perch your lips is another phrase for curl your lips.
The wave velocity vector is parallel to the cross product of the electric and magnetic vectors.If you crank a wood screw from the Electric-field direction to the Magnetic-field direction, the screw proceedsinto the wood in the direction of the wave's velocity vector.Here's another advanced and highly technical way to keep these directions straight ...Curl the fingers of your right hand in the direction FROM the electric vector TO the magnetic vector.Your right thumb (when extended) points in the direction of the waves velocity vector, and alsothe "Poynting Vector"; that's the direction in which the wave carries energy.
Longitudinal waves are scalar waves with the divergence of the vector vibration, Del.dEv/cdt . Transverse waves are vector waves with the curl of the vector vibration, DelxdEv/cdt
Cold weather can cause citrus leaves to curl and so can water stress. Aphids are another cause.