Open Question
A 1.0-mm-diameter ball bearing has 2.0×10^9 excess electrons. What is the ball bearing's potential?
25. Electric Potential
Electric Potential
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How far from a 5μC charge will the potential be 100 V?
A
4.5×10−3 m
B
450 m
C
45,000 m
D
450,000 m
Verified step by step guidance1
Understand the concept of electric potential due to a point charge. The electric potential \( V \) at a distance \( r \) from a point charge \( Q \) is given by the formula: \( V = \frac{kQ}{r} \), where \( k \) is Coulomb's constant \( 8.99 \times 10^9 \text{ N m}^2/\text{C}^2 \).
Identify the given values in the problem: the charge \( Q = 5 \mu\text{C} = 5 \times 10^{-6} \text{C} \) and the potential \( V = 100 \text{ V} \).
Rearrange the formula to solve for \( r \): \( r = \frac{kQ}{V} \). This step involves isolating \( r \) on one side of the equation.
Substitute the known values into the rearranged formula: \( r = \frac{(8.99 \times 10^9 \text{ N m}^2/\text{C}^2)(5 \times 10^{-6} \text{C})}{100 \text{ V}} \).
Calculate the expression to find the distance \( r \). This involves performing the arithmetic operations to solve for \( r \).
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