GATE EE 2022 | Electrostatics Question 8 | Electromagnetic Fields

GATE EE 2022

MCQ (Single Correct Answer)

-0.67

As shown in the figure below, to concentric conducting spherical shells, centred at r = 0 and having radii r = c and r = d are maintained at potentials such that the potential V(r) at r = c is V₁ and V(r) at r = d is V₂. Assume that V(r) depends only on r, where r is the radial distance. The expression for V(r) in the region between r = c and r = d is

GATE EE 2022 Electromagnetic Fields - Electrostatics Question 10 English

$$V(r) = {{cd({V_2} - {V_1})} \over {(d - c)r}} - {{{V_1}c + {V_2}d - 2{V_1}d} \over {d - c}}$$

$$V(r) = {{cd({V_1} - {V_2})} \over {(d - c)r}} + {{{V_2}d - {V_1}c} \over {d - c}}$$

$$V(r) = {{cd({V_1} - {V_2})} \over {(d - c)r}} - {{{V_1}c - {V_2}c} \over {d - c}}$$

$$V(r) = {{cd({V_2} - {V_1})} \over {(d - c)r}} - {{{V_2}c - {V_1}c} \over {d - c}}$$

GATE EE 2021

Numerical

-0

Consider a large parallel plate capacitor. The gap $d$ between the two plates is filled entirely with a dielectric slab of relative permittivity 5 . The plates are initially charged to a potential difference of V volts and then disconnected from the source. If the dielectric slab is pulled out completely, then the ratio of the new electric field $E_2$ in the gap to the original electric field $E_1$ is $\_\_\_\_$ .

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GATE EE 2018

Numerical

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The capacitance of an air-filled parallel-plate capacitor is 60 pF. When a dielectric slab whose thickness is half the distance between the plates, is placed on one of the plates covering it entirely, the capacitance becomes 86 pF. Neglecting the fringing effects, the relative permittivity of the dielectric is _____________ (up to 2 decimal places).

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GATE EE 2017 Set 2

Numerical

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A thin soap bubble of radius R = 1 cm, and thickness a = 3.3 µm(a << R), is at a potential of 1 V with respect to a reference point at infinity. The bubble bursts and becomes a single spherical drop of soap (assuming all the soap is contained in the drop) of radius r. The volume of the soap in the thin bubble is $$4\mathrm{πR}^2\mathrm a$$ and that of the drop is $$\frac43\mathrm{πr}^3$$. The potential in volts, of the resulting single spherical drop with respect to the same reference point at infinity is __________. (Give the answer up to two decimal places.) GATE EE 2017 Set 2 Electromagnetic Fields - Electrostatics Question 36 English