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BITSAT 2016
Exam
BITSAT
Year
2016
Subject
Physics
Chapter
Electrostatics

BITSAT 2016 · Physics · Electrostatics

The surface charge density of a thin charged disc of radius R is σ...

The surface charge density of a thin charged disc of radius R\mathrm{R} is σ\sigma. The value of the electric field at the centre of the disc is σ2ϵ0\frac{\sigma}{2 \epsilon_{0}}. With respect to the field at the centre, the electric field along the axis at a distance R\mathrm{R} from the centre of the disc⁡\operatorname{disc}

Options

  1. Areduces by 70.7%70.7 \%
  2. Breduces by 29.3%29.3 \%
  3. Creduces by 9.7%9.7 \%
  4. Dreduces by 14.6%14.6 \%

Correct answer

A. reduces by 70.7%70.7 \%

Step-by-step solution

Electric field intensity at the centre of the disc. (\mathrm{E}=\frac{\sigma}{2 \epsilon_{0}} \text{ (given) }) Electric field along the axis at any distance xx from the centre of the disc (\mathrm{E}^{\prime}=\frac{\sigma}{2 \epsilon_{0}} \left(1-\frac{\mathrm{x}}{\sqrt{\mathrm{x}^{2}}-\mathrm{R}^{2}}\right)) From question, (x=R\mathrm{x}=\mathrm{R}) (radius of disc) (∴E′=σ2ϵ0(1−RR2+R2)=σ2ϵ0(2R−R2R)=414E\begin{aligned} &\therefore E^{\prime}=\frac{\sigma}{2 \epsilon_{0}} \left(1-\frac{R}{\sqrt{R^{2}+R^{2}}}\right)\\ &=\frac{\sigma}{2 \epsilon_{0}} \left(\frac{\sqrt{2} R-R}{\sqrt{2} R}\right)\\ &=\frac{4}{14}E \end{aligned}) (\therefore) \% reduction in the value of electric field (=(E−414E)×100E=100014(=\frac{\left(\mathrm{E}-\frac{4}{14} \mathrm{E}\right) \times 100}{\mathrm{E}}=\frac{1000}{14}\%=70.7 \%)
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