1. The problem statement, all variables and given/known data The following problem from Griffiths is irritating me for a long time… A toroidal coil has a rectangular cross section, with inner radius a, outer radius a+w, and height h. It carries a total of N tightly bound wound turns, and the current is increasing at a constant rate dI/dt=k.If w and h are both much less than a, find the electric field at a point z above the centre of the toroid. [Griffiths gives hint: exploit the analogy between Faraday fields and magnetostatic fields.] 2. Relevant equations Maxwell's equations!!! 3. The attempt at a solution Here are the two ways I approached the problem. 1. For each turn of wire, a rectangular loop may be assumed. For dI/dt, the magnetic flux Φ (=∫B∙da ) is increasing. So, induced emf ∫E∙dl = ξ = (-dФ/dt ). Using standard expression of B (=μNI/2πs) (in the circumferential direction) inside the loop, I got --- ξ = [(μ(N^2)hk)/2π] ln[(a+w)/a] I understand that this closed line integral is evaluated around the rectangular loop. But I need to evaluate e field at the top of the toroid axis…Is there any way out? 2. Griffiths approach: E can be evaluated from divE=0 and curl E= (-∂B/∂t) and E→ 0 at ∞. Well, I still do not know how to find E(z) specified. I tried with a trick: taking curl of (curl of E) in LHS and curl of B in RHS. So that the LHS reduces to laplacian of E and from that a Poisson like equation should follow. However, the RHS got zero!!! So this is the case. Please help and note that I need to understand the mathematics in physical terms.