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Answer :
Final answer:
The charge on the glass bead is calculated by using the formula for the electric potential due to a point charge and considering the potential difference between two points at different distances from the charge. Solving for the charge yields a value of 2.84 nC.
Explanation:
We need to calculate the charge on the glass bead using the potential difference and the distances given. To find the charge (Q) on the bead, we use the formula for the electric potential (V) due to a point charge, which is
V = kQ/r,
where k is Coulomb's constant (k approximately equals 8.99 × 109 N·m2/C2), Q is the charge, and r is the distance from the charge.
Given the potential difference (ΔV) of 460 V between the points 1.70 mm and 4.30 mm from the bead, we set up the equation
ΔV = V1 - V2
= kQ(1/r1 - 1/r2).
Solving for Q, we find:
Q = ΔV / (k × (1/r1 - 1/r2))
= 460 V / (8.99 × 109 N·m2/C2 × (1/0.0017 m - 1/0.0043 m))
= 460 V / (8.99 × 109 × 0.1497 m-1)
= 2.84 × 10-9 C
= 2.84 nC.
Therefore, the charge on the bead is 2.84 nC (nanocoulombs).
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