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Two metallic spheres of radii 1 cm and 3 cm are given charges of -1 × 10-2 C and 5 × 10-2 C, respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is
- a)2 × 10–2 C
- b)3 × 10–2 C
- c)4 × 10–2 C
- d)1 × 10–2 C
Correct answer is option 'B'. Can you explain this answer?
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We need to find the electric potential at the surface of the larger sphere due to the smaller sphere.
Given data:
Radius of smaller sphere, r1 = 1 cm
Radius of larger sphere, r2 = 3 cm
Charge on smaller sphere, q1 = -1 µC
Charge on larger sphere, q2 = -3 µC
Permittivity of free space, ε0 = 8.854 × 10^-12 F/m
We know that the electric potential due to a point charge q at a distance r from it is given by:
V = kq/r
where k is the Coulomb constant, k = 1/4πε0 = 8.99 × 10^9 Nm^2/C^2
For a charged sphere of radius R, the electric potential at a distance r from its center is given by:
V = kq(R^2/r)
If we want to find the electric potential at the surface of the larger sphere due to the smaller sphere, we need to put r = R2 = 3 cm and q = q1 = -1 µC in the above equation:
V = kq1(R2^2/R2) = -kR2q1 = -8.99 × 10^9 × 0.03 × (-1 × 10^-6) = 269.7 V
Therefore, the electric potential at the surface of the larger sphere due to the smaller sphere is 269.7 V.
Given data:
Radius of smaller sphere, r1 = 1 cm
Radius of larger sphere, r2 = 3 cm
Charge on smaller sphere, q1 = -1 µC
Charge on larger sphere, q2 = -3 µC
Permittivity of free space, ε0 = 8.854 × 10^-12 F/m
We know that the electric potential due to a point charge q at a distance r from it is given by:
V = kq/r
where k is the Coulomb constant, k = 1/4πε0 = 8.99 × 10^9 Nm^2/C^2
For a charged sphere of radius R, the electric potential at a distance r from its center is given by:
V = kq(R^2/r)
If we want to find the electric potential at the surface of the larger sphere due to the smaller sphere, we need to put r = R2 = 3 cm and q = q1 = -1 µC in the above equation:
V = kq1(R2^2/R2) = -kR2q1 = -8.99 × 10^9 × 0.03 × (-1 × 10^-6) = 269.7 V
Therefore, the electric potential at the surface of the larger sphere due to the smaller sphere is 269.7 V.
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Two metallic spheres of radii 1 cm and 3 cm are given charges of -1 × 10-2 C and 5 × 10-2 C, respectively. If these are connected by a conducting wire, the final charge on the bigger sphere isa)2 × 10–2 Cb)3 × 10–2 Cc)4 × 10–2 Cd)1 × 10–2 CCorrect answer is option 'B'. Can you explain this answer?
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