Given below are two statements, one labelled as Assertion (A) and the other labelled as Reason (R). In the light of these statements, choose the most appropriate answer from the options given below.
Assertion (A): Gauss's law in magnetostatics and in electrostatics is, respectively, ∮ B · dS = 0 and ∮ E · dS = q(enclosed)/ε₀.
Reason (R): Magnetic monopoles do not exist, whereas electric monopoles (isolated charges) exist.
- ABoth (A) and (R) are true and (R) is the correct explanation of (A)
- BBoth (A) and (R) are true but (R) is not the correct explanation of (A)
- C(A) is false but (R) is true
- D(A) is true but (R) is false
Show answer and explanation
Correct answer: (a) Both (A) and (R) are true and (R) is the correct explanation of (A)
Explanation
Both statements are true, and (R) explains (A).
Gauss's law says that the flux of a field through any closed surface depends on what is enclosed:
- for the electric field, ∮ E · dS = q(enclosed)/ε₀, because isolated charges (electric monopoles) exist and a closed surface can enclose a net charge;
- for the magnetic field, ∮ B · dS = 0, because magnetic monopoles have never been found. Magnetic field lines always form closed loops, so as many lines leave a closed surface as enter it.