An electric field is expressed in rectangular coordinates by E = 6x2ax + 6y ay +4az V/m. Find:a) VMN if point M and N are specified by M(2,6,1) and N(-3, -3, 2).b) VM if V = 0 at Q(4, -2, -35)c) VN if V = 2 at P(1,2,4).Please show all steps

The values of the potential differences for the three questions are;

A)

B) = -120 V

C)

We are given the expression of the electric field as;

E = (6x² x^ + 6y y^ +4 z^) V/m

Integrating this with the M and N coordinates as boundaries in mind gives;

Plugging in those boundary values and solving using an online integral calculator gives;

Plugging in those boundary values and solving using an online integral calculator gives;

= -120 V

C) We are told that V = 2 at P(1,2,4). Thus potential difference between point V and N is;

Plugging in those boundary values and solving using an online integral calculator gives;

Thus;

= 2 + 49

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a.) -147V

b.) -120V

c.) 51V

Explanation:

a.) Equation for potential difference is the integral of the electrical field from a to b for the voltage V_ba = V(b)-V(a).

b.) The problem becomes easier to solve if you draw out the circuit. Since potential at Q is 0, then Q is at ground. So voltage across V_MQ is the same as potential at V_M.

c.) Same process as part b. Draw out the circuit and you'll see that the potential a point V_N is the same as the voltage across V_NP added with the 2V from the other box.

Honestly, these things take practice to get used to. It's really hard to explain this.

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explanation: