For a charged spherical ball, electrostatic potential inside the ball varies with r as V = 2 a r 2 + b . Here, a and b are constant and r is the distance from the center. The volume charge density inside the ball is - λ a ε . The

Question

For a charged spherical ball, electrostatic potential inside the ball varies with r as V = 2 a r 2 + b . Here, a and b are constant and r is the distance from the center. The volume charge density inside the ball is - &#955; a &#949; . The value of &#955; is ______. &#949; = permittivity of medium.

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As we know, E = - d V d r = - 4 a r Now, electric field inside the charged sphere is given by E = &#961; r 3 &#949; . Comparing both, we get &#961; = - 12 a &#949; . Therefore, &#955; = 12 .

For a charged spherical ball, electrostatic potential inside the ball varies with r as V = 2 a r 2 + b . Here, a and b are constant and r is the distance from the center. The volume charge density inside the ball is - λ a ε . The value of λ is ______. ε = permittivity of medium.

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More from Electrostatics

For a charged spherical ball, electrostatic potential inside the ball varies with r as V = 2 a r 2 + b . Here, a and b are constant and r is the distance from the center. The volume charge density inside the ball is - &#955; a &#949; . The value of &#955; is ______. &#949; = permittivity of medium.

Correct answer

Step-by-step solution

More from Electrostatics

For a charged spherical ball, electrostatic potential inside the ball varies with r as V = 2 a r 2 + b . Here, a and b are constant and r is the distance from the center. The volume charge density inside the ball is - λ a ε . The value of λ is ______. ε = permittivity of medium.