Question

find the flux through the disc

Answer 1

Answer:

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Answer 2

Answer:

The flux through the disc is equal to q/10ε₀

Explanation:

• The flux through the disc is flux due to the shaded region.  
• To find OA (see the attach figure below),

         For right angle triangle ΔAOB,

                         $OA=\sqrt{{OB}^2+{AB}^2}$

                                 $=\sqrt{(\frac{4R}{3})^{2} + R^{2}$

                                 $=\frac{5R}{3}$

• The angle  $cos\alpha =\frac{OA}{OB}=\frac{4}{5}$

• The sold angle = $2\pi (1-cos\alpha )$

                                    = $2\pi (1-\frac{4}{5} )$

                                    = $\frac{2\pi }{5}$

• We know that, flux through 4π solid angle = q/ε₀

         flux through 2π/5 solid angle = q/10ε₀

    Thus, the flux through  the disc will be q/10ε₀.