Im having problems with this question. Can someone help me? Demonstrate your kno

Question

Im having problems with this question. Can someone help me?
Demonstrate your knowledge of how electric fields are related toelectric potentials. (a) What is the electric field E(r) = E(x, y,z) for the potential 2 2 2 V (x, y, z) = Ax + By Cz ?(Please remember that E is a vector with three components.) Thenevaluate E(r) at the point r = (2, 1, 3), with A = ½ , B = 2and C = 1. (b) What is the potential V(x) for an electric fieldEx(x) = E0 cos kx? Assume that Ey = Ez = 0, and that V0 =V(0) = E0 / k. Express your answer in terms of E0 and k. (Note thatthe quantity k here is not Coulomb’s constant, but is insteadthe wave number and has a value of
k=2/ with units of m1.)

Explanation / Answer

E = - del V = - 222 V ( A i + Bj + C k) =  -( 111 i + 444 j+ 222 k) V V(x) = - integral E dx = - E0 / k sin k x +C   where C = V(0) / k

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