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gradient of electric field

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Hello!

I try to obtain the gradient of electric field, but I fail to enter the right formula. Can sombody help me with the formula for the gradient of electric field?

Thanks!

12 Replies Last Post 2016年10月28日 GMT-4 18:17
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago 2010年4月17日 GMT-4 03:27
Hi

Well for me, if E is the electric field, in Comsol notation for EC/ES physics we have:

Ex_... = -dV/dx , Ey_... = -dV/dy , Ez_... = -dV/dz,

So if you want the elelctric field gradient we need one more deivative, and Exx .. is not in the list

so I do not see any other way than

Exx_... = d(Ex_...,x) , Exy_... = d(Ex_...,y) ...

(replace _... by your application id)

by using the special operator d( variable_name , space_variable_name )
see Guide.pdf p163 and thereon (V3.5a)

and from thereon it should be straight forward, or have I missed an important point ?

Have fun Comsoling
Ivar
Hi Well for me, if E is the electric field, in Comsol notation for EC/ES physics we have: Ex_... = -dV/dx , Ey_... = -dV/dy , Ez_... = -dV/dz, So if you want the elelctric field gradient we need one more deivative, and Exx .. is not in the list so I do not see any other way than Exx_... = d(Ex_...,x) , Exy_... = d(Ex_...,y) ... (replace _... by your application id) by using the special operator d( variable_name , space_variable_name ) see Guide.pdf p163 and thereon (V3.5a) and from thereon it should be straight forward, or have I missed an important point ? Have fun Comsoling Ivar

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Posted: 1 decade ago 2010年4月27日 GMT-4 10:18
Yes, it is correct. But in Comsol E is -Vx, that mean electric field is the negative of potential gradient. I don't now how to write the gradient of electric field. The electric field in comsol have the notation normE, and the gradient of electric field to x then it's normEx?

Thanks!!
Yes, it is correct. But in Comsol E is -Vx, that mean electric field is the negative of potential gradient. I don't now how to write the gradient of electric field. The electric field in comsol have the notation normE, and the gradient of electric field to x then it's normEx? Thanks!!

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Posted: 1 decade ago 2010年4月28日 GMT-4 01:18
Doesn't diff() work it for you? As an example, diff(normE,x) would return you the x-derivative of electric field's norm.
Doesn't diff() work it for you? As an example, diff(normE,x) would return you the x-derivative of electric field's norm.

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Posted: 1 decade ago 2010年4月28日 GMT-4 01:20
By the way, in case it is needed, normE is only an absolute scalar value and not the Electric field itself.
By the way, in case it is needed, normE is only an absolute scalar value and not the Electric field itself.

Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago 2010年4月28日 GMT-4 01:47
Hi

Sorry for the confusion, you are perfectly right, (I was at home and had no direct access to Comsol to check, and I'm the one claiming one should always verify what one is doing ;)

Hope I have corrected it now

Ivar
Hi Sorry for the confusion, you are perfectly right, (I was at home and had no direct access to Comsol to check, and I'm the one claiming one should always verify what one is doing ;) Hope I have corrected it now Ivar

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Posted: 1 decade ago 2010年4月28日 GMT-4 05:41
So,
In Comsol language:
If E on x is Ex_...=-Vx then the derivatives of Ex is Exx_... = d(Ex_...,x) . I don't understend how to write correct this derivatives in Comsol language, because I don’t have succes to obtain results.
So, In Comsol language: If E on x is Ex_...=-Vx then the derivatives of Ex is Exx_... = d(Ex_...,x) . I don't understend how to write correct this derivatives in Comsol language, because I don’t have succes to obtain results.

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Posted: 1 decade ago 2010年4月28日 GMT-4 05:43
With diff(normE,x) it not return the x-derivative of electric field's norm. I don't now where it's the problem.

Thanks!
With diff(normE,x) it not return the x-derivative of electric field's norm. I don't now where it's the problem. Thanks!

Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago 2010年4月28日 GMT-4 07:12
Hi

Simply do a surface plot your X field, something like

Ex_...

then adapt by typing your formula to

d(Ex_...,X)

check the upper/lower cas of x, it depends on you application mode and and you variable names

its d(,) and not diff(,) (as in Maple), check you guide.pdf on the special operators, thre are several that one should learn to use in there

Good luck
Ivar

Hi Simply do a surface plot your X field, something like Ex_... then adapt by typing your formula to d(Ex_...,X) check the upper/lower cas of x, it depends on you application mode and and you variable names its d(,) and not diff(,) (as in Maple), check you guide.pdf on the special operators, thre are several that one should learn to use in there Good luck Ivar

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Posted: 1 decade ago 2010年4月28日 GMT-4 08:34
Ostahie,

Adding to what Ivar said, check out what names your electric field variables are pre-assigned in the specific application mode you are working. I usually look it out in the post-processing window for selecting which field value to plot. For e.g., if you are using 2D boundary mode analysis module for TM waves, then there is a pre-defined tangential electric field variable called tEy_rfwb. If you want to take its derivative along y-direction, just write diff(tEy_rfwb,y)

The reason why you might be getting error is that there is no such variable as normE. I mentioned it only as a case example and not because it actually exists in any of the application modes.

Hope this helps.
Ostahie, Adding to what Ivar said, check out what names your electric field variables are pre-assigned in the specific application mode you are working. I usually look it out in the post-processing window for selecting which field value to plot. For e.g., if you are using 2D boundary mode analysis module for TM waves, then there is a pre-defined tangential electric field variable called tEy_rfwb. If you want to take its derivative along y-direction, just write diff(tEy_rfwb,y) The reason why you might be getting error is that there is no such variable as normE. I mentioned it only as a case example and not because it actually exists in any of the application modes. Hope this helps.

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Posted: 1 decade ago 2010年4月28日 GMT-4 15:42
Shakeeb,

normE_emdc=sqrt(abs(Ex_emdc)^2+abs(Ey_emdc)^2), where Ex_emdc=-Vx an Ey_emdc=-Vy.

If the derivatives of normE_emdc on x is dEx=diff(normE_emdc,x) , and the derivatives of normE_emdc on y is dEy=diff(normE_emdc,y) then gradient of electric field is gradE=sqrt(dEx^2+dEy^2).
My reasoning is correct?

Thanks!!!





Shakeeb, normE_emdc=sqrt(abs(Ex_emdc)^2+abs(Ey_emdc)^2), where Ex_emdc=-Vx an Ey_emdc=-Vy. If the derivatives of normE_emdc on x is dEx=diff(normE_emdc,x) , and the derivatives of normE_emdc on y is dEy=diff(normE_emdc,y) then gradient of electric field is gradE=sqrt(dEx^2+dEy^2). My reasoning is correct? Thanks!!!

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Posted: 1 decade ago 2010年4月28日 GMT-4 15:54
So far as I see, the equation of gradE you specify is just the 'norm' of the gradient of electric field's 'norm' :)

If this is the quantity that interests you in the specific circumstance you are working in then that is fine. Otherwise, I don't think it is a standard practice to call this formulation of gradE as the gradient of electric field.

Please remember that gradient operator works on scalar fields to produce a vector field which provides the measure of how the 'scalar' field varies in different spatial directions. Since electric field is a vector field, what generally seems more meaningful to me is to specify the gradient of various components of electric field.
So far as I see, the equation of gradE you specify is just the 'norm' of the gradient of electric field's 'norm' :) If this is the quantity that interests you in the specific circumstance you are working in then that is fine. Otherwise, I don't think it is a standard practice to call this formulation of gradE as the gradient of electric field. Please remember that gradient operator works on scalar fields to produce a vector field which provides the measure of how the 'scalar' field varies in different spatial directions. Since electric field is a vector field, what generally seems more meaningful to me is to specify the gradient of various components of electric field.

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Posted: 8 years ago 2016年10月28日 GMT-4 18:17
I am trying to plot ∇E^2.
For Electric field distribution of my design (in r, phi,z) coordinates, i used the following equation:

sqrt(es2.Er*es2.Er+es2.Ephi*es2.Ephi+es2.Ez*es2.Ez)

How do i plot the 'Gradient of Eelctric field square' if that is what it should be called i.e. ∇E^2.

The quantity should have units of V^2/m^3.

Let me know.
I am trying to plot ∇E^2. For Electric field distribution of my design (in r, phi,z) coordinates, i used the following equation: sqrt(es2.Er*es2.Er+es2.Ephi*es2.Ephi+es2.Ez*es2.Ez) How do i plot the 'Gradient of Eelctric field square' if that is what it should be called i.e. ∇E^2. The quantity should have units of V^2/m^3. Let me know.

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