A uniformly charged hemisphere of radius b and charge density ρ has a hemispherical cavity of radius a(a = (b/2)) cut from its centre. If the potential at the centre of the cavity is (n ρ b2/16 ∈ 0) then n=?

Question

A uniformly charged hemisphere of radius b and charge density ρ has a hemispherical cavity of radius a(a = (b/2)) cut from its centre. If the potential at the centre of the cavity is (n ρ b2/16 ∈ 0) then n=? <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-bx1s0aeunw8q.png" /> (A) 3 (B) 4 (C) 5 (D) 6

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/795daee7766d59611fa3960965954359-.png" /> V= displaystyle ∫ ab (K (2 π x2 d x) ρ /x) V=2π kρ [(b2 - a2/2)]=π ρ k(b2 - a2) b=2a v=3π kρ b2

Q. A uniformly charged hemisphere of radius $b$ and charge density $ρ$ has a hemispherical cavity of radius $a (a = \frac{b}{2})$ cut from its centre. If the potential at the centre of the cavity is $\frac{n ρ b ^{2}}{16 \in _{0}}$ then $n = ?$

3

4

5

6

$V = \int_{a}^{b} \frac{K ( 2 π x ^{2} d x ) ρ}{x}$
$V = 2 πk ρ [\frac{b ^{2} - a ^{2}}{2}] = π ρ k (b^{2} - a^{2})$
$b = 2 a$
$v = 3 πk ρ b^{2}$

Q. A uniformly charged hemisphere of radius b and charge density ρ has a hemispherical cavity of radius a(a=2b​) cut from its centre. If the potential at the centre of the cavity is 16∈0​nρb2​ then n=?

3

4

5

6

V=∫ab​xK(2πx2dx)ρ​ V=2πkρ[2b2−a2​]=πρk(b2−a2) b=2a v=3πkρb2

Q. A uniformly charged hemisphere of radius $b$ and charge density $ρ$ has a hemispherical cavity of radius $a (a = \frac{b}{2})$ cut from its centre. If the potential at the centre of the cavity is $\frac{n ρ b ^{2}}{16 \in _{0}}$ then $n = ?$

$V = \int_{a}^{b} \frac{K ( 2 π x ^{2} d x ) ρ}{x}$
$V = 2 πk ρ [\frac{b ^{2} - a ^{2}}{2}] = π ρ k (b^{2} - a^{2})$
$b = 2 a$
$v = 3 πk ρ b^{2}$