# A question about cruel and electric fields?

#### sagar474

Joined Jul 22, 2010
16

is curl of a study electric field is zero in every case ?

then how the expression
delXE=-dB/dt

that is an electric field can produce a time varying magnetic field ?

how the time varying magnetic field is related to delxE with out involving time variable on left side of the equation.​

#### Papabravo

Joined Feb 24, 2006
20,604
You fail to appreciate the implication of Maxwell's equation that changing electric fields produce magnetic fields, and changing magnetic fields produce electric fields.

If the curl of the electric field is zero it means the electric field, E, is not changing. This is identical to the situation in mechanics where not accelerating can mean either standing still or moving with a uniform velocity.

If you work through the vector algebra it should be obvious that if the magnetic field depends linearly on time then the partial derivative of the magnetic field , B, with respect to time is independent of time.

Traveling waves in one dimension are often described as functions of (x + ct) or (x - ct), where c is the speed of light. The curl of E is a vector with three components and the partial derivative of B with respect to t, is also a vector with three components. If both of those vectors are equal to the same set of three constants then we have satisfied the requirement.

• logearav

#### BillO

Joined Nov 24, 2008
999
Electric fields can be many things, but cruel?

They have never been cruel to me. Edit: Just making light...no offense intended

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#### Wendy

Joined Mar 24, 2008
23,320
English is not the OPs first language, so be nice. I wonder what he meant though.

#### MrChips

Joined Oct 2, 2009
29,848
Read his post. He meant "curl".

#### Papabravo

Joined Feb 24, 2006
20,604
The curl of a vector field, E is represented by del cross E

$$\nabla \times E$$

The expansion of the above expression is a vector in 3 dimensions.

• logearav

#### BillO

Joined Nov 24, 2008
999
is curl of a study electric field is zero in every case ?

then how the expression
delXE=-dB/dt

that is an electric field can produce a time varying magnetic field ?

how the time varying magnetic field is related to delxE with out involving time variable on left side of the equation.​
E is a time depndent vector function.

One could write:

$$E\ =\ F(x, y, z, t) \ such\ that, \ \nabla\ X\ E =\ V(x,y,z,t),\ another\ time\ dependent\ vector\ function \ We\ also\ find\ that, \ B\ =\ G(x, y, z, t) \ such\ that, \ - \frac{\partial B}{\partial t}\ =\ V(x,y,z,t)$$

Aside: Sorry about the formatting. It seems that the \emph and \textbf tags do not work in this latex interpreter. It makes it difficult to express vectors the common accepted way. My guess is someone thought having them was a little too spicy. "White bread, with a little water on the side for dippin'" is enough for us, thanks.

• logearav