Question

two conducting spheres of radii r1 and r2 have same electric field near their surfaces. the ratio of.their electric potential​

Answer 1

Explanation

Both the spheres have the same surface charge densities.

Let us suppose that the sphere with radius R1 has a charge q1 on it, and that the sphere with radius R2 has a charge q2 on it.

Now,

q1/[4π(R1)²] = q2/[4π(R2)²]

=> q1/R1² = q2/R2²

=> q1/q2 = (R1/R2)²

Potential in first sphere = V1 = kq1/R1

Potential on second sphere = V2 = kq2/R2

Thus, V1/V2 = q1.R2/q2.R1 = (q1/q2).(R2/R1)=(R1/R2).

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Answer 2

Answer:

Ratio = r₁ / r₂

Explanation:

Given:

• Two conducting spheres of radii r₁ and r₂.
• Have same electric field.

To find,

• Ratio of their electric potential.

Solution:

•   Electric field on the surface of conducting sphere = kQ / R²

 

• according to given condition,

               ie., having same electric field

• kq₁ /r₁² = kq₂ /r₂²
• q₁ /r₁² =  q₂ /r₂²
• q₁ /q₂ = r₁² /r₂² --------------- (1)
• ratio of potentials at centre
• kq₁ /r₁²÷  kq₂ /r₂² = q₁ /q₂ .  r₁² /r₂²
• substituting q₁ /q₂ from (1)
• we get

   Ratio = r₁ / r₂

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