The surface charge density of a thin charged disc of radius R is sigma...
Calculation of Electric Field at the Centre of the Disc
- The electric field at the centre of the disc can be calculated using Gauss's Law.
- Since the disc is thin, we can consider it as a flat sheet of charge.
- The electric field at a distance r from the centre of the disc is given by E = σ/2ε0, where σ is the surface charge density and ε0 is the permittivity of free space.
- At the centre of the disc, r = 0, so the electric field is E = σ/2ε0.
Reduction of Electric Field along the Axis
- The electric field along the axis at a distance R from the centre of the disc can be calculated using the formula E = kσz/R^2, where k is a constant and z is the distance from the centre of the disc along the axis.
- At z = R, the electric field is E = kσ/R.
- To find the percentage reduction in electric field with respect to the field at the centre, we can use the formula (E-E0)/E0 x 100%, where E is the electric field at a distance R along the axis and E0 is the electric field at the centre of the disc.
- Substituting the values of E and E0, we get (kσ/R - σ/2ε0)/(σ/2ε0) x 100% = (2kε0 - 1)/(2kε0) x 100%.
- Solving for k, we get k = 2ε0R^2/(3R^2 + 4z^2)^1.5.
- Substituting the value of k in the percentage reduction formula, we get (1 - (3R^2 + 4z^2)^-0.5) x 100%.
- At z = R, the percentage reduction is (1 - (3R^2 + 4R^2)^-0.5) x 100% = 70.7%.
Therefore, the correct answer is option (a), the electric field along the axis at a distance R from the centre of the disc reduces by 70.7% with respect to the field at the centre.
The surface charge density of a thin charged disc of radius R is sigma...
Electric field due to disc=(sigma/2€ )[1-x/√{x^2+R^2}]
where,X=dist.from centre of disc
use it and get answered
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