What is the electric potential halfway between a charge of 7.25x10-9 C and another of 4.00x10-9 C charge separated by 100.0 cm?
Answer (2)
Calculate the electric potential V 1 due to charge q 1 at the midpoint using the formula V 1 = r k q 1 .
Calculate the electric potential V 2 due to charge q 2 at the midpoint using the formula V 2 = r k q 2 .
The total electric potential V at the midpoint is the sum of the individual potentials: V = V 1 + V 2 .
Substitute the given values and calculate the numerical value of V , which is approximately 202 V .
202 V
Explanation
Problem Analysis We are asked to find the electric potential at the midpoint between two charges. We will calculate the electric potential due to each charge at the midpoint and then add them to find the total electric potential.
Electric Potential Formula The electric potential due to a point charge is given by the formula: V = r k q where:
V is the electric potential,
k is Coulomb's constant ( 8.99 × 1 0 9 N ⋅ m 2 /C 2 ),
q is the charge, and
r is the distance from the charge to the point of interest.
Given Values We have two charges:
q 1 = 7.25 × 1 0 − 9 C
q 2 = 4.00 × 1 0 − 9 C The distance between the charges is 100.0 cm = 1.00 m. The midpoint is at a distance of r = 1.00 m /2 = 0.50 m from each charge.
Calculating Individual Potentials The electric potential due to q 1 at the midpoint is: V 1 = r k q 1 = 0.50 m ( 8.99 × 1 0 9 N ⋅ m 2 / C 2 ) ( 7.25 × 1 0 − 9 C ) V 1 = 0.50 8.99 × 7.25 V = 130.345 V The electric potential due to q 2 at the midpoint is: V 2 = r k q 2 = 0.50 m ( 8.99 × 1 0 9 N ⋅ m 2 / C 2 ) ( 4.00 × 1 0 − 9 C ) V 2 = 0.50 8.99 × 4.00 V = 71.92 V
Total Electric Potential The total electric potential at the midpoint is the sum of the individual potentials: V = V 1 + V 2 = 130.345 V + 71.92 V = 202.265 V Rounding to three significant figures, we get V = 202 V .
Final Answer The electric potential halfway between the two charges is approximately 202 V.
Examples
Understanding electric potential is crucial in many real-world applications. For instance, in designing electronic circuits, engineers need to calculate the electric potential at various points to ensure the circuit functions correctly. Similarly, in medical devices like ECG machines, the electric potential generated by the heart is measured to diagnose heart conditions. The principles used in this problem are fundamental to these applications.
To find the electric potential halfway between the two charges, we calculated the individual potentials from each charge at the midpoint and summed them up. The electric potential due to charge q 1 is approximately 130.345 V, and due to charge q 2 is approximately 71.92 V, leading to a total of approximately 202 V. Therefore, the electric potential halfway between the two charges is approximately 202 V.
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