For a charged spherical ball, electrostatic potential inside the ball… | JEE Main 2023 (29 Jan, Shift 2)

Q64JEE Main 2023 · 29 JAN · SHIFT 2Medium

Electric Potential & Equipotentials

For a charged spherical ball, electrostatic potential inside the ball varies with $r$ as $V = 2ar^2 + b$ . Here, $a$ and $b$ are constant and r is the distance from the center. The volume charge density inside the ball is $-\lambda a\varepsilon$ . The value of $\lambda$ is ____________.

$\varepsilon$ = permittivity of the medium

Numerical answer type. Work it out, then open the answer.

Show answer and solution

Answer: 12

$E = -\dfrac{dV}{dr} = -4ar$
Gauss's law inside a uniform ball: $E = \dfrac{\rho r}{3\varepsilon}$
$\dfrac{\rho r}{3\varepsilon} = -4ar \Rightarrow \rho = -12a\varepsilon$
So $\lambda = 12$ .

Report a mistake

More questions on Electric Potential & Equipotentials

A charged spherical conductor of radius ' R ' is connected momentarily to another…MHT CET 2023 (13 May, Shift 1)
Two isolated metallic solid spheres of radii R and 2R are charged such that both have…JEE Main 2023 (30 Jan, Shift 1)
Assume that an electric field E = 30x²i exists in space. If ' V₀ ' is the potential at…MHT CET 2023 (10 May, Shift 2)
Three concentric spherical metallic shells X, Y and Z of radius a, b and c respectively…JEE Main 2023 (10 Apr, Shift 1)
Two hollow conducting spheres of radii R1 and R2 (R1 >> R2) have equal charges. The…NEET 2022 (Phase 1)
27 identical drops are charged at 22V each. They combine to form a bigger drop. The…JEE Main 2022 (25 Jun, Shift 2)
If the electric potential at any point (x, y, z) m in space is given by V = 3x2 volt. The…JEE Main 2022 (29 Jun, Shift 2)
The angle between the electric lines of force and the equipotential surface isNEET 2022 (Phase 1)

Electric Potential & Equipotentials question from JEE Main 2023 (29 Jan, Shift 2)

More questions on Electric Potential & Equipotentials