This document solves two problems regarding Faraday's and Ampere's laws of electromagnetism. It first finds the magnetic field B that satisfies Faraday's law given an electric field E. It then determines if the same E and B fields satisfy Ampere's law by checking if their electric fields are equal, finding they are not, so the pair do not satisfy both laws.

1. Problem 3.4 (N.N. Rao, Elements of Engineering Electromagnetics, 6th
Edition)
Given: ;
Find
(a)B that satisfies Faraday’s Law in differential form
Solution:
(b) Determine if the pair of E and B satisfies Ampere’s Circuital Law in differential form
Let E’ be the Electric Field of Ampere’s Circuital Law
Solution:

2. Since the electric fields are not equal, . The pair of fields E and B satisfies only Faraday’s Law,
while the pair E’ and B satisfies only Ampere’s Circuital Law. Thus, the answer is no.