Question 186: Electrostatics & Capacitance

Question

Electric charge is transferred to an irregular metallic disk as shown in the figure. If $\sigma_1$, $\sigma_2$, $\sigma_3$ and $\sigma_4$ are charge densities at given points then, choose the correct answer from the options given below: A. $\sigma_1>\sigma_3 ; \sigma_2=\sigma_4$ B. $\sigma_1>\sigma_2 ; \sigma_3>\sigma_4$ C. $\sigma_1>\sigma_3>\sigma_2=\sigma_4$ D. $\sigma_1<\sigma_3<\sigma_2=\sigma_4$ E. $\sigma_1=\sigma_2=\sigma_3=\sigma_4$

Accepted Answer

Therefore, the relationship between charge density and ROC at different points can be expressed as:
$ \sigma \propto \frac{1}{\mathrm{ROC}} $
From this, the relationship between the charge densities at the specified points becomes clear:
$ (\mathrm{ROC})_1  \sigma_3 > \sigma_2 = \sigma_4 $
Thus, the charge density is greatest at the point with the smallest ROC and decreases as the ROC increases, keeping in mind that $\sigma_2$ and $\sigma_4$ have equal ROC, hence equal charge densities.

Answer

B and C Only

Answer

A and C Only

Answer

D and E Only

Answer

A, B and C Only

Electrostatics & Capacitance

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