KVPY SX SB Exam 20141 Question Paper

Question : 34 of 120

Marks: +1, -0

Consider a spherical shell of radius R with a total charge +Q uniformly spread on its surface (center of the shell lies at the origin x = 0). Two point charges, +q and -q are brought, one after the other, from far away and placed at

x = -a/2

and

x= +a/2 (a < R)

, respectively. Magnitude of the work done in this process is

$( Q + q)^2/{ 4πε_0a}$
zero
$q^ 2/{ 4πε_0a}$
${Qq}/{ 4πε_0a}$

Validate

Solution:

PE_i

= Initial energy of system =

Q^ 2/{ 8πε_0a}

(self energy of shell)

PE_\f

= Final energy of system =

Q^ 2/{ 8πε_0a}+{q×(-q)}/{4πε_0a}+{kQ×q}/R+{kQ(-q)}/R

⇒Q^ 2/{ 8πε_0a}-q^2/{4πε_0a}

(self energy of shell) (Interaction energy between various charges)
Work done =

PE_\f - PE_i

={-q^2}/{4πε_0a}

Magnitude of work done =

{q^2}/{4πε_0a}

Go to Question:

Prev Question

Next Question