Question:
Among the following, the incorrect Maxwell's Electromagnetic equation is
Among the following, the incorrect Maxwell's Electromagnetic equation is
Show Hint
Remember:
\[
\oint \vec{B}\cdot d\vec{A}=0
\]
because isolated magnetic charges (magnetic monopoles) do not exist.
Updated On: Jun 25, 2026
- \[ \oint \vec{B}\cdot d\vec{l} = \mu_0 i_c+\mu_0\varepsilon_0\frac{d\phi_E}{dt} \]
- \[ \oint \vec{B}\cdot d\vec{A} = \frac{Q}{\varepsilon_0} \]
- \[ \oint \vec{E}\cdot d\vec{l} = -\frac{d\phi_B}{dt} \]
- \[ \oint \vec{E}\cdot d\vec{A} = \frac{Q}{\varepsilon_0} \]
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The Correct Option is B
Solution and Explanation
Step 1: Recall Maxwell's equations.
The four Maxwell equations are: \[ \oint \vec{E}\cdot d\vec{A} = \frac{Q}{\varepsilon_0} \] (Gauss law for electricity) \[ \oint \vec{B}\cdot d\vec{A}=0 \] (Gauss law for magnetism) \[ \oint \vec{E}\cdot d\vec{l} = -\frac{d\phi_B}{dt} \] (Faraday's law) \[ \oint \vec{B}\cdot d\vec{l} = \mu_0 i_c+\mu_0\varepsilon_0\frac{d\phi_E}{dt} \] (Ampere-Maxwell law)
Step 2: Compare the given options.
Option (1) is correct because it represents Ampere-Maxwell law.
Option (3) is correct because it represents Faraday's law of electromagnetic induction.
Option (4) is correct because it represents Gauss law for electricity.
Option (2) is incorrect because \[ \oint \vec{B}\cdot d\vec{A} \] must always be zero: \[ \oint \vec{B}\cdot d\vec{A}=0 \] Magnetic monopoles do not exist.
Step 3: Final conclusion.
Hence, the incorrect Maxwell equation is \[ \boxed{ \oint \vec{B}\cdot d\vec{A} = \frac{Q}{\varepsilon_0} } \]
The four Maxwell equations are: \[ \oint \vec{E}\cdot d\vec{A} = \frac{Q}{\varepsilon_0} \] (Gauss law for electricity) \[ \oint \vec{B}\cdot d\vec{A}=0 \] (Gauss law for magnetism) \[ \oint \vec{E}\cdot d\vec{l} = -\frac{d\phi_B}{dt} \] (Faraday's law) \[ \oint \vec{B}\cdot d\vec{l} = \mu_0 i_c+\mu_0\varepsilon_0\frac{d\phi_E}{dt} \] (Ampere-Maxwell law)
Step 2: Compare the given options.
Option (1) is correct because it represents Ampere-Maxwell law.
Option (3) is correct because it represents Faraday's law of electromagnetic induction.
Option (4) is correct because it represents Gauss law for electricity.
Option (2) is incorrect because \[ \oint \vec{B}\cdot d\vec{A} \] must always be zero: \[ \oint \vec{B}\cdot d\vec{A}=0 \] Magnetic monopoles do not exist.
Step 3: Final conclusion.
Hence, the incorrect Maxwell equation is \[ \boxed{ \oint \vec{B}\cdot d\vec{A} = \frac{Q}{\varepsilon_0} } \]
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