Need step by step solutions with answers: 1. The electric potential of a charge

Question

Need step by step solutions with answers:

1. The electric potential of a charge distribution is given by the equation: V(x) = 3x^2y^2 + yz^3 - 2z^3x, where x, y, z are measured in meters and V is measured in volts. Find the magnitude and direction of the electric field vector as a funciton of x,y, and z. Use i, j, k notaiton in your answer to completely describe the field.

2. A thin rod of length 2L is oriented on the x-axis with its center at the orgin. The rod carries a total charge Q distributed uniformly over its length. Determine the potential V as a function of y for points along the y axis > 0. Assume V=0 at infinity.

Explanation / Answer

1. Ex=dV/dx (only partial derivative)=6xy^2-2z^3

Ey=6x^2y+z^3

Ez=3yz^2-6xz^2

E=(6xy^2-2z^3)i+(6x^2y+z^3)j+(3yz^2-6xz^2)k

2)V(y)=Integral(k*(Q/2L)dx/(sqrt(x^2+y^2), from x=-L to L)= Integral(k*(Q/L)dx/(sqrt(x^2+y^2), from x=0 to L)

=(kQ/L)ln(sqrt(y^2+x^2)+L)

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