Maxwell-s four equations are written asi - E - d s - q 0 - 0ii - B - d s -0iii - E - d l - d dt - B - d siv - B - d s - 0 - 0 d dt - E - d sOut of the four Maxwell-s equation above- which one shows the non-existence of monopoles-

The correct option is B (ii) onlyHad there been a monopole, the integral of B⃗.d⃗s⃗ on a closed surface enclosing the monopole would have been non zero.T ...

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Standard XII

Physics

Symmetry in Laws

Maxwell's fou...

Question

Maxwell's four equations are written as
(i) $\oint \to E . \to d s = \frac{q_{0}}{ε_{0}}$
(ii) $\oint \to B . \to d s = 0$
(iii) $\oint \to E . \to d l = \frac{d}{d t} \oint \to B . \to d s$
(iv) $\oint \to B . \to d s = μ_{0} ε_{0} \frac{d}{d t} \oint \to E . \to d s$
Out of the four Maxwell's equation above, which one shows the non-existence of monopoles?

(i) and (iv)

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(ii) only

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(iii) only

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none of these

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Solution

The correct option is B (ii) only
Had there been a monopole, the integral of $\to B . \to d s$ on a closed surface enclosing the monopole would have been non-zero.
Thus the second equation shows the non-existence of monopole.

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Similar questions

Maxwell's four equations are written as

(i)

\oint \to E . \to d s = \frac{q_{0}}{ε_{0}}

(ii)

\oint \to B . \to d s = 0

(iii)

\oint \to E . \to d l = \frac{d}{d t} \oint \to B . \to d s

(iv)

\oint \to B . \to d s = μ_{0} ε_{0} \frac{d}{d t} \oint \to E . \to d s

Which of the above Maxwell's equations shows that electric field lines do not form closed loops?

Q. Consider the following two Maxwell's equations.

(i)

\oint \to E . d \to A = \frac{q_{in}}{ϵ_{0}}

(i i)

\oint \to E . d \to l = - \frac{d ϕ_{B}}{d t}

The electric fields

\to E

, mentioned in both the equations, are -

Q. (a) Write Gauss' law for magnetism in the form of Maxwell's equation.
(b) Write the value of

\frac{1}{\sqrt{μ_{0} ε_{0}}}

Q. One of Maxwell's Equations can be written as

\oint \to B . d \to A = 0

.
Which of the following statements follows directly from this statement? Select two answers.

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Maxwell's four equations are written as(i) ∮→E.→ds=q0ε0(ii)∮→B.→ds=0(iii)∮→E.→dl=ddt∮→B.→ds(iv)∮→B.→ds=μ0ε0ddt∮→E.→dsOut of the four Maxwell's equation above, which one shows the non-existence of monopoles?

The correct option is B (ii) onlyHad there been a monopole, the integral of →B.→ds on a closed surface enclosing the monopole would have been non-zero.Thus the second equation shows the non-existence of monopole.

The correct option is B (ii) only
Had there been a monopole, the integral of $\to B . \to d s$ on a closed surface enclosing the monopole would have been non-zero.
Thus the second equation shows the non-existence of monopole.