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GUJCET · Physics · Electrostatic Potential and Capacitance
Consider three concentric shells of metal A , B and C are having radii a, b and c respectively as shown in the figure. \((a<b<c)\). Their surface charge densities are \(\sigma,-\sigma\) and \(\sigma\) respectively. Calculate the electrical potential on the surface of shell A .
- A \(\frac{\sigma}{\varepsilon_0}(a-b-c)\)
- B \(\frac{\sigma}{\varepsilon_0}(a+b-c)\)
- C \(\frac{\sigma}{\varepsilon_0}(a-b+c)\)
- D \(\frac{\sigma}{\varepsilon_0}\left(a^2+b^2+c^2\right)\)
Answer & Solution
Correct Answer
(C) \(\frac{\sigma}{\varepsilon_0}(a-b+c)\)
Step-by-step Solution
Detailed explanation
(C)
\(\begin{array}{l} V _{ A }= V _a+ V _b+ V _c \\ V_{ A }=\frac{1}{4 \pi \varepsilon_0}\left[\frac{q_a}{a}+\frac{q_b}{b}+\frac{q_c}{c}\right]\end{array}\)
\(\begin{aligned} V _{ A }=\frac{1}{4 \pi \varepsilon_0}\left[\frac{4 \pi a^2 \sigma}{a}\right. & +\frac{4 \pi b^2(-\sigma)}{b} \\ & \left.+\frac{4 \pi c^2(\sigma)}{c}\right]\end{aligned}\)
\(V _{ A }=\frac{\sigma}{\varepsilon_0}[a-b+c]\)
\(\begin{array}{l} V _{ A }= V _a+ V _b+ V _c \\ V_{ A }=\frac{1}{4 \pi \varepsilon_0}\left[\frac{q_a}{a}+\frac{q_b}{b}+\frac{q_c}{c}\right]\end{array}\)
\(\begin{aligned} V _{ A }=\frac{1}{4 \pi \varepsilon_0}\left[\frac{4 \pi a^2 \sigma}{a}\right. & +\frac{4 \pi b^2(-\sigma)}{b} \\ & \left.+\frac{4 \pi c^2(\sigma)}{c}\right]\end{aligned}\)
\(V _{ A }=\frac{\sigma}{\varepsilon_0}[a-b+c]\)
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