# Can the Curl of an electric field (which is constant) be non zero?

This was the solution to problem 4.30 in Griffiths 'Introduction to electrodynamics ' .

In it he asks ' An electric dipole p, pointing in the y direction, is placed midway between two large conducting plates, as shown . Each plate makes a small angle θ with respect to the x axis, and they are maintained at potentials ±V . What is the direction of the net force on p? '

While I understand his solution, I have a problem with the way he's drawn the field lines . They curl around . While I believe that all electric fields should have zero curl . Even with Stokes theorem the closed loop integral for this would be non zero according to the figure .

Where am I going wrong in my analysis ?

• Would you please clarify why you think the curl is non-zero in this case? It's not because the electric field lines are curved is it?. Note that curl can be non-zero for an electric field with field lines that are straight, e.g., $\mathbf{E} = y\mathbf{\hat{x}}$ – Alfred Centauri Feb 2 '18 at 13:52
• I think the curl is zero not just because of the intuition from the diagram but also because if we took the loop integral according to Stoke's Theorem the curl would turn out as non zero . Also according to Griffith (Electrodynamics) pg 78 ' E=yx̂ could not possibly be an electrostatic field; no set of charges, regardless of their sizes and positions, could ever produce such a field' – Ishita Gupta Feb 3 '18 at 12:35
• Let me try a different approach: describe how the electric field lines in the diagram should look in order to satisfy your intuition that the curl is zero. – Alfred Centauri Feb 3 '18 at 13:28

The electric field between the capacitor plates is an electrostatic field, which is equivalent to having a zero curl: $$curl \vec E =0$$ The depiction of the electric field lines between the tilted capacitor plates, however, seems not to be correct. They are equidistant. The density of the field lines, which is a measure of the electric field strength, should decrease to the right (in x-direction). This has probably caused you the problems you mentioned. That the field lines are bent is, in itself, not an indication that the $curl \vec E \neq 0$\$ Think of the field lines between a positive and a negative point charge. They are also curved.