Concentric metallic hollow spheres of radii R and 4 R hold charges Q 1 and Q 2 respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference V ( R )- V (4 R ) is:

Question

Concentric metallic hollow spheres of radii R and 4 R hold charges Q 1 and Q 2 respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference V ( R )- V (4 R ) is: (A) (3 Q 1/16 π ε0 R ) (B) ( Q 2/4 π ε0 R ) (C) (3 Q 1/4 π ε0 R ) (D) (3 Q 2/4 π ε0 R )

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/27648db4324637f3443546e440eeac8d-.png" /> E=(K Q1/r2) Δ V=∫ limitsR4 R E dr=(3 K Q1/4R)

Q. Concentric metallic hollow spheres of radii $R$ and $4 R$ hold charges $Q_{1}$ and $Q_{2}$ respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference $V (R) - V (4 R)$ is:

$\frac{3 Q _{1}}{16 π ε _{0} R}$

$\frac{Q _{2}}{4 π ε _{0} R}$

$\frac{3 Q _{1}}{4 π ε _{0} R}$

$\frac{3 Q _{2}}{4 π ε _{0} R}$

$E = \frac{K Q _{1}}{r ^{2}}$
$Δ V = R \int 4 R E d r = \frac{3 K Q _{1}}{4 R}$

Q. Concentric metallic hollow spheres of radii R and 4R hold charges Q1​ and Q2​ respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference V(R)−V(4R) is:

16πε0​R3Q1​​

4πε0​RQ2​​

4πε0​R3Q1​​

4πε0​R3Q2​​