Question

Two thin spherical shells, one with radius R and the other with radius 2R, surround an isolated
charged point particle. The ratio of the number of field lines through the larger sphere to the
number through the smaller is:
A. 1
B. 2
C. 4.
D. 1/2
E. 1/4​

Answer 1

Answer:

----> 2R/ R

----->. 2/1

------> 2

hope this helps

Answer 2

Answer:

The ratio of the number of field lines through the larger sphere to the number of field lines through the smaller is $\frac{1}{4}$ i.e.option(E).

Explanation:

The electric field for a spherical shell is given as,

$E=\frac{kQ}{R^2}$       (1)

Where,

E=electric field of a spherical shell

Q=point charge

k=coulomb's constant

R=radius of the spherical shell

Also, The number of field lines through the spherical shell is directly proportional to the electric field. So, the ratio of electric fields will be equal to the number of field lines passing through the sphere.

From the question we have,

R₁=R

R₂=2R

We can write equation (1) as,

$\frac{E_2}{E_1} =\frac{R_1^2}{R_2^2}$          (2)

By substituting the values of R₁ and R₂ in equation (2) we get;

$\frac{E_2}{E_1} =\frac{R^2}{(2R)^2}$

$\frac{E_2}{E_1}=\frac{1}{4}$    

Hence, the ratio of the number of field lines through the larger sphere to the number of field lines through the smaller is $\frac{1}{4}$ i.e.option(E).