Correct Response: C. According to Maxwell's third equation (Faraday's law), an electric field that varies with time will always give rise to a magnetic field that also varies with time. Response A comes from Maxwell's second equation (Gauss's law for magnetism), which states that the total magnetic flux through a surface is equal to zero (A) for closed surfaces. This has nothing to do with producing a time dependent magnetic field. A time-dependent magnetic field is not produced from the gradient of a scalar function (B); it is produced by a time-dependent electric field. According to Maxwell's first law (Gauss's law for electric fields), the electric flux through a surface is zero (D) for any closed surface that contains no charges. This does not give rise to a time-dependent magnetic field.
