Hey i was wondering about a paticular problem i found in a text book. Specifically just one little niggle i have with it.(adsbygoogle = window.adsbygoogle || []).push({});

i am given that the electrostatic potential energy in a region of space is given by

v(r) = ((q*n)/(epsilon-0))(x^2+y^2)

(where n is a constant of dimensions m^-3)

It then goes on to say calculate the electric field, so E= -grad(V)

since v is a scalar field then grad(v) is simply

-gradv = E = -( d/dx (v)i+ d/dy (v)j+ d/dy (v)k)

and in this case the d/dx is a partial derivitive.

So i have to partial differeniate V with respect to all co-ords and then stick a vector on each direction respective of what its been differentiated by.

But i have a problem, the n is a constant so it's constant througout the region of space, but does it get differentiated?

common sense says no as to keep the dimensions required for an electric field E it'd need to have 1/distance^2 as the actual final units of distance (after cancelling the quotants)

and not differenctiating the n would make this so.

BUT im unsure as i rarely trust common sense with physics anymore :P especially since starting quantum physics this year :(.

Thanks guys

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# Electromagnetism, vector calculus.

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