Physics - Electrostatics Question with Solution | TestHub

PhysicsElectrostaticsElectric Field & ForceHard2 minPYQ_2016

PhysicsHardsingle choice

The region between two concentric spheres of radii 'a' and 'b', respectively (see figure), has volume charge density $ρ = \frac{A}{r}$ , where A is a constant and r is the distance from the centre. At the centre of the spheres is a point charge Q. The value of A such that the electric field in the region between the spheres will be constant, is:

Options:

Answer:

Solution:

${E=E}_{1} + E_{2}$

$⇒E = \frac{K [Q + \int_{a}^{r} 4 π x^{2} d x \frac{A}{x}]}{r^{2}}$

$E = K [\frac{Q}{r^{2}} + 4 π A \{\frac{r^{2}}{2 r^{2}} - \frac{a^{2}}{2 r^{2}}\}]$

$\frac{d E}{d r} = 0$

$\Rightarrow - 2 \frac{Q}{r^{3}} + \frac{8 π A a^{2}}{2 r^{3}} = 0$

$A = \frac{Q}{2 π a^{2}}$

Stream:JEESubject:PhysicsTopic:ElectrostaticsSubtopic:Electric Field & Force

⏱ 2mℹ️ Source: PYQ_2016

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