mathrm{R} ત્રિજ્યા ધરાવતા ગોળા પર વિજભારઘનતા | vedclass

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Question

Fill the empty space with $+\rho$ and $-\rho$ charge density.

$\left|\mathrm{E}_{\mathrm{A}}\right|=0+\frac{\operatorname{k\rho} \cdot \frac{4}{3}

Vedclass · Accepted Answer

$\frac{18}{34}$

Vedclass · Answer

Fill the empty space with $+\rho$ and $-\rho$ charge density.

$\left|\mathrm{E}_{\mathrm{A}}\right|=0+\frac{\operatorname{k\rho} \cdot \frac{4}{3} \pi\left(\frac{\mathrm{R}}{2}\right)^{3}}{\left(\frac{\mathrm{R}}{2}\right)^{2}}=\operatorname{k\rho} \frac{4}{3} \pi\left(\frac{\mathrm{R}}{2}\right)$

$\left|\mathrm{E}_{\mathrm{B}}\right|=\frac{\mathrm{k} \rho \cdot \frac{4}{3} \pi \mathrm{R}^{3}}{\mathrm{R}^{2}}-\frac{\mathrm{k} \rho \cdot \frac{4}{3} \pi\left(\frac{\mathrm{R}}{2}\right)^{3}}{\left(\frac{3 \mathrm{R}}{2}\right)^{2}}$

$=\operatorname{k\rho} \frac{4}{3} \pi \mathrm{R}-\mathrm{k} \rho \frac{4}{3} \pi \frac{\mathrm{R}}{18}=\mathrm{k} \rho \cdot \frac{4}{3} \pi\left(\frac{17 \mathrm{R}}{18}\right)$

$\frac{E_{A}}{E_{B}}=\frac{9}{17}=\frac{18}{34}$

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