question_answer

Direction: Q.11 to Q.15

By analogy to Gauss's law of electrostatics, we can write Gauss's law of magnetism as \[\oint{\overrightarrow{B}\cdot \overrightarrow{d\,S}={{\mu }_{0}}{{m}_{inside}}}\] where \[\oint{\overrightarrow{B}\cdot \overrightarrow{d\,S}}\] is the magnetic flux and \[{{m}_{inside}}\] is the net pole strength inside the closed surface.

We do not have an isolated magnetic pole in nature. At least one has been found to exist till date. The smallest unit of the source of magnetic field is a magnetic dipole where the net magnetic pole is zero. Hence, the net magnetic pole enclosed by any closed surface is always zero.

Correspondingly, the flux of the magnetic field through any closed surface is zero.

Read the given passage carefully and give answer of the following questions:

Consider the two idealised systems

(i) A parallel plate capacitor with large plates and small separation and

(ii) a long solenoid of length L>>R, radius of cross-section.

In (i) \[\overrightarrow{E}\] is ideally treated as a constant between plates and zero outside. In (ii) magnetic field is constant inside the solenoid and zero outside. These idealised assumptions, however, contradict fundamental laws as below:

A) case (i) contradicts Gauss's law for electrostatic fields.

B) case (ii) contradicts Gauss's law for magnetic fields.    

C) case (i) agrees with \[\oint{\overrightarrow{E}\cdot \overrightarrow{dl}=0}\].

D) case (ii) contradicts \[\oint{\overrightarrow{E}\cdot \overrightarrow{dl}={{l}_{en}}}\].