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Two Charged Spherical Conductors of Radii R1 and R2 When Connected by a Conducting Wire Acquire Charges q1 and q2 Respectively. Find the Ratio of Their Surface Charge Densities in Terms of Their Radii. - Physics

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ConceptConductors and Insulators Related to Electric Field

Question

Two charged spherical conductors of radii R1 and R2 when connected by a conducting wire acquire charges q1 and q2 respectively. Find the ratio of their surface charge densities in terms of their radii.

Solution

 
 

The surface charge density for a spherical conductor is given by:

`sigma=Q/(4pir^2)`

For spherical conductor R1, the surface charge density is given by:

`sigma_1=q_1/4piR_(1^2)`

Similarly, for spherical conductor R2, the surface charge density is given by:

`sigma_2=q_2/(4piR_(2^2))`

`:.sigma_1/sigma_2=(q_1/q_2)((R_(2^2))/R_(1^2))`

Since the two conductors are connected, we have:

q1=q2

`:.sigma_1/sigma_2=R_(2^2)/R_(1^2)`

 
 
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Solution Two Charged Spherical Conductors of Radii R1 and R2 When Connected by a Conducting Wire Acquire Charges q1 and q2 Respectively. Find the Ratio of Their Surface Charge Densities in Terms of Their Radii. Concept: Conductors and Insulators Related to Electric Field.
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