The wave eqn for a prticle in non conducting or free soace is given by Laplacian(E)=u*e*partial double derivative of (E) with respect to time
where E is the electric field
u,e are the permiability and permitivity of free space.

Now my question is laplacian(X)=Divergence(Gradient of X)
now X is a scalar Quantity here how can we take gradient of Electric Field E which is a vector quantity??

my email
the_coolest_@rediffmail.com

 

Originally posted by the_coolest_@Mar 31 2005, 03:28 PM
The wave eqn for a prticle in non conducting or free soace is given by Laplacian(E)=u*e*partial double derivative of (E) with respect to time
where E is the electric field
u,e are the permiability and permitivity of free space.

Now my question is laplacian(X)=Divergence(Gradient of X)
now X is a scalar Quantity here how can we take gradient of Electric Field E which is a vector quantity??

my email
the_coolest_@rediffmail.com

[post=6624]Quoted post[/post]​

Forget about vectors for a moment and go back to calc. The gradient is just a set of derivitives in the end. One in the x, one in the y and one in the z.

If you take the derivatve of a scalar function, you get a scalar derivative.
4x+6y-8z=0
4(dx/dt)+6(dy/dt)-8(dz/dt)=0

If you take the derivatve of a vector function, you get a vector derivative.
4x i + 6y j - 8z k=0
4(dx/dt) i +6(dy/dt) j - 8(dz/dt) k=0

A derivative or an integral doesn't not change the scalar or vector function type, it only operates on the coefficients and the varibiles. Not the direction.

 

Originally posted by Brandon@Mar 31 2005, 07:30 PM
Forget about vectors for a moment and go back to calc. The gradient is just a set of derivitives in the end. One in the x, one in the y and one in the z.

If you take the derivatve of a scalar function, you get a scalar derivative.
4x+6y-8z=0
4(dx/dt)+6(dy/dt)-8(dz/dt)=0

If you take the derivatve of a vector function, you get a vector derivative.
4x i + 6y j - 8z k=0
4(dx/dt) i +6(dy/dt) j - 8(dz/dt) k=0

A derivative or an integral doesn't not change the scalar or vector function type, it only operates on the coefficients and the varibiles. Not the direction.

[post=6626]Quoted post[/post]​

my qs is tht gradient always operates on a scalar quantity and produces a vector quantity. the direction is decided by the maximum rate of change of tht scalar quantity.

now a vector already has a direction. how can i find the maximum rate of change of a vector???

if X is a scalar then in cartesian coordinate system then its gradient is given by
d(X)/dx i +d(X)/dy j +d(X)/dz k
where d/dx,d/dy,d/dz are the partial derivatives wrt x,y,z