MTEL Physics Practice Exam

Category - Physics

According to Maxwell's equations, a time-dependent magnetic field will be produced under which of the following circumstances?
  1. The total magnetic flux through a surface is equal to zero.
  2. A field exists that is the gradient of a scalar function.
  3. An electric field varies with time.
  4. The electric flux through surface is zero.
Explanation
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.
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