Ncert Exercises & Solutions

Consider the two idealized systems (i) a parallel plate capacitor with large plates and small separation and (ii) a long solenoid of length L>>R, the radius of the cross-section. In (i) E is ideally treated as a constant between plates and zero outside. In (ii) the magnetic field is constant inside the solenoid and zero outside. These idealized assumptions, however, contradict fundamental laws as below:

1. case (i) contradicts Gauss' law for electrostatic fields
2. case (ii) contradicts Gauss' law for magnetic fields
3. case (i) agrees with $\oint E . d l = 0$
4. case (ii) contradicts $\oint H \cdot d I = I_{e n}$

(b) Hint: Use Gauss law for the electric field as well as for the magnetic field.

Step 1: As Gauss' law states,

\oint_{S} E \cdot d s = \frac{q}{ε_{0}}

for the electrostatic field. It does not contradict electrostatic fields as the electric field lines do not form a continuous closed path.

Step 2: According to Gauss' law in the magnetic field,

\oint E \cdot d s = 0

It contradicts for the magnetic field because there is a magnetic field inside the solenoid and no field outside the solenoid carrying current but the magnetic field lines form the closed path.

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