Question
Which of Maxwell’s equations allows for the calculation of a magnetic field due to a changing electric field?
(A) \(\oint E.dA=\frac{q}{\varepsilon _{0}}\)
(B) \(\oint E.d\varphi =\frac{d\phi _{B}}{dt}\)
(C) \(\oint B.dA=0\)
(D) \(\oint B.d\varphi =\mu_{o}i+\mu _{o}\varepsilon _{o}\frac{d\phi _{E}}{dt}\)
(E) None of the above
Answer/Explanation
Ans: D
Question
A large parallel-plate capacitor is being charged and the magnitude of the electric field between the plates of the capacitor is increasing at the rate dE/dt. Which of the following statements is correct about the magnetic field in the region between the plates of the charging capacitor?
A) It is parallel to the electric field.
B) Its magnitude is directly proportional to dE/dt.
C) Its magnitude is inversely proportional to dE/dt.
D) Nothing about the field can be determined unless the charging current is known.
E) Nothing about the field can be determined unless the instantaneous electric field is known.
Answer/Explanation
Ans.B
Solution
From Ampere-Maxwell’s equation, the effect of a changing electric field between the plates of a charging capacitor are identical in the production of a magnetic field as a current through a wire
Question
One of Maxwell’s equations can be written as \(\phi\) E • ds = – \(\frac{d\phi }{dt}\). This equation expresses the fact that
(A) a changing magnetic field produces an electric field
(B) a changing electric field produces a magnetic field
(C) the net magnetic flux through a closed surface depends on the current inside
(D) the net electric flux through a closed surface depends on the charge inside
(E) electric charge is conserved