A charge is distributed over two concentric hollow

Question

A charge is distributed over two concentric hollow spheres of radii r and R where R>r , such that the surface densities of charges are equal .what is potential at their common centre

Zachariah Abraham · Accepted Answer

By superposition princpiple, potential at the common centre is equal to algebraic sum of potentials at centre due to each sphere.

If we want the potential of a sphere, we need the radius (given) and the charge on it (which is what we should find now).

If the total charge is Q, then let’s assume charge of small sphere si q1, and large sphere is q2.

Thus $Q = q1 + q2$

It is given that the surface charge density is the same, thus:
$(q1)/(4*pi*r^2) = (q2)/(4*pi*R^2).$

Therefore,

$q1 = (r^2)(q2)/(R^2)$

But $q1 + q2 = Q,$

therefore,

$q2 = Q(R^2)/(r^2 + R^2),$

and similarly (from the same equation,

$q1 = Q(r^2)/(r^2 + R^2).$

Potential at common centre is now given as:

$k(q1)/r + k(q2)/R.$

Substituting previously found values, this becomes:

$k(Q)(r+R)/(r^2 + R^2).$

If you found this answer helpful, be sure to approve it as the right answer!

Electrostatics> A charge is distributed over two concentr...

A charge is distributed over two concentric hollow spheres of radii r and R where R>r , such that the surface densities of charges are equal .what is potential at their common centre

Aniket , 8 Years ago

Zachariah Abraham

Rishi Sharma

LIVE ONLINE CLASSES

Electrostatics question based on earthing of spherical shell

electrostatics

an object has a charge of 2c and gains 10^19 electrons. the net chaarge on the object becomes??

electrostatics

A wire with a linear charge density lambda forms a quarter of a cjrclenof radius R and is placed asa shown in thefigure with its centre of curvature at the origin O the electric field at O will be

electrostatics

Find the value of q so that system remains in equilibrium.. figure attached below

electrostatics

Need to find the time taken for the dipole to come back to eqm

electrostatics

Electrostatics> A charge is distributed over two concentr...

A charge is distributed over two concentric hollow spheres of radii r and R where R>r , such that the surface densities of charges are equal .what is potential at their common centre

Aniket , 8 Years ago

Zachariah Abraham

Rishi Sharma

LIVE ONLINE CLASSES

Other Related Questions on electrostatics

Electrostatics question based on earthing of spherical shell

electrostatics

an object has a charge of 2c and gains 10^19 electrons. the net chaarge on the object becomes??

electrostatics

A wire with a linear charge density lambda forms a quarter of a cjrclenof radius R and is placed asa shown in thefigure with its centre of curvature at the origin O the electric field at O will be

electrostatics

Find the value of q so that system remains in equilibrium.. figure attached below

electrostatics

Need to find the time taken for the dipole to come back to eqm

electrostatics