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Q.Write down Maxwell equations in integral form. OR Derive the equation for angle of deviation produced by a prism.

Tamil Nadu DgeTamil Nadu HSC (DGE) Board 2026Subjective· 5mImportance★★★★★
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(a) Maxwell's four equations in integral form unify Gauss's laws (electric and magnetic), Faraday's law, and the Ampere-Maxwell law; (b) a prism's refractive index follows from its minimum-deviation geometry, n=sin⁡[(A+Dm)/2]/sin⁡(A/2)n=\sin[(A+D_m)/2]/\sin(A/2). Both alternatives answered below.

(a) Maxwell's equations in integral form

1. Gauss's law for electricity. The total electric flux through any closed surface equals 1/ε01/\varepsilon_0 times the enclosed charge:

∮E⃗⋅dA⃗=qencε0\oint \vec E\cdot d\vec A = \dfrac{q_{enc}}{\varepsilon_0}

2. Gauss's law for magnetism. The total magnetic flux through any closed surface is always zero (no isolated magnetic monopoles exist; field lines always form closed loops):

∮B⃗⋅dA⃗=0\oint \vec B\cdot d\vec A = 0

3. Faraday's law of electromagnetic induction. The line integral of the electric field around any closed loop equals minus the rate of change of magnetic flux through it:

∮E⃗⋅dl⃗=−dΦBdt\oint \vec E\cdot d\vec l = -\dfrac{d\Phi_B}{dt}

4. Ampere-Maxwell law. The line integral of the magnetic field around any closed loop equals μ0\mu_0 times the sum of the conduction current and the displacement current enclosed:

∮B⃗⋅dl⃗=μ0Ienc+μ0ε0dΦEdt\oint \vec B\cdot d\vec l = \mu_0 I_{enc} + \mu_0\varepsilon_0\dfrac{d\Phi_E}{dt}

Together, these four equations fully describe classical electromagnetism, and their mutual coupling (a changing BB creates EE, and a changing EE creates BB) predicts self-sustaining electromagnetic waves travelling at c=1/μ0ε0c=1/\sqrt{\mu_0\varepsilon_0}.

(b) Angle of deviation and refractive index of a prism

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