- #1
David23454
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Homework Statement
In a certain region, the electric potential due to a charge distribution
is given by the equation V (x, y, z) = (3x2y2+yz3-2z3x)V0/a4 where
a, x, y, and z are measured in meters and V and V0 are in volts. What
is the magnitude of the electric field at the position (x, y, z) = (a, a, a)?
Homework Equations
[/B]
E=-(dV/dx(i)+dV/dy(j)+dV/dz(k))
The Attempt at a Solution
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Taking the negative derivative of V(x,y,z) and inputing "a" gives E=-V0/a(4,7,-3)
I would have thought that this was the complete solution, but the solution that goes on to absval(E)=V0/a(42+72+32)½
=V0/a(74)½
I haven't taken multi-variable calculus yet (it wasn't a requirement for the course), so I'm a little confused as to what's going on in the part where the absolute value of E is equal to V0/a4(2+72+32)½. Could someone explain to me how this works, specifically, why should I take the abs value of E, and add up the squares of the derivatives and then take their square root to get the answer? Thanks!