I need help please this is due in less than an hour. thanks D mandan University

Question

I need help please this is due in less than an hour. thanks

D mandan University Physics II Homework Worksheet 1 Name: Section: An electric potential function is given by where MKS units are used. Show all work neatly. Don't forget to include units in your answers. Use the back if more room is needed, but note accordingly 1. What is the electric field vector, E(r,y), in rectangular coordinates? 2. What is the magnitude and direction of the electric field at the point (x,y) (2,3)? 3. What is the divergence of the electric field at the point (x.y) (2,3)? 4. What is the curl of the electric field at the point (x.y) (2,3)?

Explanation / Answer

(1) First of all to calcualte the Electric field from potential

since the potential is given in X, Y coordinate only therefore we neglect Z coordinate here.

now on differentiation

Ex= - (3y2-4xy) , EY = -(6xy-2x2)

(2) E = Ex+ EY = -(3y2 -4xy) i + (-(6xy-2x2))j

For point (2,3) put x=2, and y = 3

E= -3i -28 j

E= 28.16 N/C and its direction tan(angle) = (28/3)

angle = 83.88

(3) Now for divergence of electric field, we multipled the electric field by this del operator.

Div(E) =4y i -6x j

on putting the value of x and Y

Div(E)= 12i - 12 j

(4) Now for curl

On solving this determinat we will get curl (E) = -12i + 18 j

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