Determine the charge of the sphere if the potential at a point located 50 cm from the surface of the sphere is 4 V. The radius of the sphere is 5 cm.
We translate all the values from given to the SI system:
l = 50 cm. = 0.5 m.
R = 5 cm. = 0.05 m.
Potential of a field point located at a distance from r center of the sphere:
φ = q / (4π * ε0 * r), where q is the magnitude of the sphere’s charge, r is the distance from the center of the sphere to the point of the field, ε0 is the electrical constant ε0 = 8.85 * 10 ^ -12 F / m.
Distance from the center of the sphere to the point of the field with potential φ:
r = R + l.
Substitute in the expression to determine the potential:
φ = q / (4π * ε0 * r) = q / (4π * ε0 * (R + l)).
Let us express from this expression – the charge:
q = φ * (4π * ε0 * (R + l).
Substitute the numerical values and determine the charge of the sphere:
q = φ * (4π * ε0 * (R + l) = 4 * (4 * π * 8.85 * 10 ^ -12 * (0.5 + 0.05) = 2.44 * 10 ^ -10 Cl …
Answer: the charge of the sphere is 2.44 * 10 ^ -10 C.
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