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uniquement dans le cas d'une distribution discrète de charges

uniquement dans le cas d'une distribution continue de charges

Temps estimé: 1 minute

En choisissant une surface de Gauss mal adapté au système chargé, le théorème de Gauss

aucune des réponses

donne toujours un champ électrique nul

devient faux

always gives a zero electric field

Estimated time: 1 minute

By choosing a Gaussian surface that is not well suited to the charged system, Gauss’s theorem:

becomes false

none of the answers

Temps estimé: 1 minute

D'après l'énoncé du théorème de Gauss, on peut affirmer que:

Si aucune charge est contenue dans la surface de Gauss,

Le flux est toujours négatif à travers cette surface

Le flux est toujours positif à travers cette surface

aucune des réponses

Le flux du champ est nul à travers cette surface

Estimated time: 1 minute

When the electric field is tangent to a part of the Gaussian surface, the flux of through the entire surface is:

maximal

minimal

none of the answers

necessarily zero

Find the critical point(s) of the function defined by .

and

Find the critical point(s) of the function defined by .

and

And let be a critical point of and the Hessian of this function at point .

Let be a function .

Check the incorrect answer.

If , is positive semi-definite, then is convex in and is a global minimum.

If is a local maximum, then is negative-definite .

If , is positive-definite, then is strictly convex in and is the only global minimum.

If , is negative semi-definite, then is concave in and is a global maximum.

25%

If is positive-definite, then is a local minimum.

If , is negative-definite, then is strictly concave in and is the only global maximum.

If is nor semi-negative-definite, nor positive semi-definite and , then is a saddle point.

Let be the function defined by .

The function is strictly convex on .

Its Hessian matrix is:

The function is neither concave nor convex.

We cannot know whether the function is convex.

The function is strictly concave on .

Let be the function defined by .

Its Hessian matrix is:

The function is neither concave nor convex.

The function is strictly convex on .

The function is strictly concave on .

We cannot know whether the function is convex.