The Moving Coil Galvanometer

Step 1: Force due to surface tension.
For a water film, force due to surface tension on each wire is where .
Step 2: Work done.
Work done in increasing separation by is
Step 3: Substitution.

Step 4: Conclusion.
The work done is .

Step 1: Electric field due to an infinite plane sheet.
For a uniformly charged infinite plane sheet, the electric field outside the sheet is given by:
where is surface charge density.

Step 2: Electric field near a charged conductor.
For a charged conductor, the electric field just outside the surface is:

Step 3: Compare the two expressions.

Step 4: Conclusion.
Hence, the correct relation is .

Step 1: Deflection in Galvanometer.
The deflection in a moving coil galvanometer is proportional to the number of turns . If the number of turns is halved, the deflection will also be halved.
Step 2: Final Answer.
Thus, the deflection for the same current will become half.

Step 1: Working principle of moving coil galvanometer.
A moving coil galvanometer uses a strong radial magnetic field produced by permanent magnets.

Step 2: Effect of stray magnetic fields.
Stray magnetic fields such as earth’s magnetic field are very weak compared to the strong field inside the galvanometer.

Step 3: Resulting effect.
Due to the dominance of the internal magnetic field, external stray fields do not cause noticeable deflection.

Step 4: Conclusion.
A stray magnetic field does not affect the galvanometer because the internal magnetic field is very strong.