Solution Found!
One of these is an impossible electrostatic field. Which
Chapter 2, Problem 20P(choose chapter or problem)
One of these is an impossible electrostatic field. Which one?
(a) \(\mathbf{E}=k[x y \hat{\mathbf{x}}+2 y z \hat{\mathbf{y}}+3 x z \hat{\mathbf{z}}]\);
(b) \(\mathbf{E}=k\left[y^{2} \hat{\mathbf{x}}+\left(2 x y+z^{2}\right) \hat{\mathbf{y}}+2 y z \hat{\mathbf{z}}\right]\).
Here k is a constant with the appropriate units. For the possible one, find the potential, using the origin as your reference point. Check your answer by computing \(\nabla V\). [Hint: You must select a specific path to integrate along. It doesn’t matter what path you choose, since the answer is path-independent, but you simply cannot integrate unless you have a definite path in mind.]
Questions & Answers
QUESTION:
One of these is an impossible electrostatic field. Which one?
(a) \(\mathbf{E}=k[x y \hat{\mathbf{x}}+2 y z \hat{\mathbf{y}}+3 x z \hat{\mathbf{z}}]\);
(b) \(\mathbf{E}=k\left[y^{2} \hat{\mathbf{x}}+\left(2 x y+z^{2}\right) \hat{\mathbf{y}}+2 y z \hat{\mathbf{z}}\right]\).
Here k is a constant with the appropriate units. For the possible one, find the potential, using the origin as your reference point. Check your answer by computing \(\nabla V\). [Hint: You must select a specific path to integrate along. It doesn’t matter what path you choose, since the answer is path-independent, but you simply cannot integrate unless you have a definite path in mind.]
ANSWER:Step 1 of 6
We have to check out of (a) and (b) which one is an impossible electrostatic field and for the possible electrostatic field we have to find the potential.
We can check for an impossible electrostatic field by evaluating \(\nabla \times E\).
For a possible electrostatic field \(\nabla \times E=0\) and for an impossible electrostatic field \(\nabla \times E \neq 0\)