Two metal spheres of radius R and 3R have same surface charge density σ. If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes σ_1 and 2,…

Question

Two metal spheres of radius R and 3R have same surface charge density σ. If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes σ_1 and 2, respectively. The ratio _1 _2 is

Accepted Answer

Correct answer: D. (d) When two conducting spheres are in contact, they achieve the same electric potential. Consider two metal spheres with radii R and 3R that have the same surface charge density . For a conductive sphere, the potential V of a sphere can be expressed as V= σr _0, where r is the radius of the sphere and _0 is the permittivity of free space. When the two spheres are brought into contact and then separated, they equalize their potentials: V_1=V_2 Thus, the equations become: _1r_1= _2r_2 Substituting for the radii: _1R= _2 (3R ) From this, we can solve for the ratio of the surface charge densities: _1 _2= 3RR=3 Therefore, the ratio of the surface charge densities on the smaller sphere to the larger sphere after contact is 3.

$Two metal spheres of radius R and 3R have same surface charge density σ. If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes σ_{1} and 2, respectively. The ratio \frac{σ _{1}}{σ _{2}} is$

Solution

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