Concept explainers
(a)
The electric potential at the origin due to single charge particle.
(a)
Answer to Problem 66AP
The electric potential at the origin due to single charge particle is
Explanation of Solution
Write the expression of the electric potential due to single point charge.
Here,
Conclusion:
Substitute
Therefore, the electric potential at the origin due to single charge particle is
(b)
The electric potential at the origin due to two charge particle.
(b)
Answer to Problem 66AP
The electric potential at the origin due to two charge particle is
Explanation of Solution
Write the expression of the electric potential due to group of point charge.
Here,
For two point chargers the above equation is given as.
Here,
Conclusion:
Substitute
Therefore, the electric potential at the origin due to two charge particle is
(c)
The electric potential at the origin due to four charge particle.
(c)
Answer to Problem 66AP
The electric potential at the origin due to four charge particle is
Explanation of Solution
Write the expression of the electric potential due to group of point charge.
Here,
For four point chargers the above equation is given as.
Here,
Conclusion:
Substitute
Therefore, the electric potential at the origin due to four charge particle is
(d)
The electric potential given by the exact expression and compare the result.
(d)
Answer to Problem 66AP
The electric potential at the origin based on exact expression is
Explanation of Solution
Write the given exact expression of electric potential.
Here,
Conclusion:
Substitute,
Thus, the electric potential based on given expression is
In all the values of electric potential in all four parts, the largest value is
Therefore, the electric potential at the origin is
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Chapter 25 Solutions
Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
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- A uniformly charged insulating rod of length 14.0 cm is bent into the shape of a semicircle as shown in Figure P20.29. The rod has a total charge of 7.50 C. Find the electric potential at O, the center of the semicircle. Figure P20.29arrow_forwardA filament running along the x axis from the origin to x = 80.0 cm carries electric charge with uniform density. At the point P with coordinates (x = 80.0 cm, y = 80.0 cm), this filament creates electric potential 100 V. Now we add another filament along the y axis, running from the origin to y = 80.0 cm, carrying the same amount of charge with the same uniform density. At the same point P, is the electric potential created by the pair of filaments (a) greater than 200 V, (b) 200 V, (c) 100 V, (d) between 0 and 200 V, or (e) 0?arrow_forwardFour particles are positioned on the rim of a circle. The charges on the particles are +0.500 C, +1.50 C, 1.00 C, and 0.500 C. If the electric potential at the center of the circle due to the +0.500 C charge alone is 4.50 104 V, what is the total electric potential at the center due to the four charges? (a) 18.0 104 V (b) 4.50 104 V (c) 0 (d) 4.50 104 V (e) 9.00 104 Varrow_forward
- Figure P26.80 shows a wire with uniform charge per unit length = 2.25 nC/m comprised of two straight sections of length d = 75.0 cm and a semicircle with radius r = 25.0 cm. What is the electric potential at point P, the center of the semicircular portion of the wire? FIGURE P26.80arrow_forwardA filament running along the x axis from the origin to x = 80.0 cm carries electric charge with uniform density. At the point P with coordinates (x = 80.0 cm, y = 80.0 cm), this filament creates electric potential 100 V. Now we add another filament along the y axis, running from the origin to y = 80.0 cm. carrying the same amount of charge with the same uniform density. At the same point P, is the electric potential created by the pair of filaments (a) greater than 200 V, (b) 200 V, (c) 100 V, (d) between 0 and 200 V, or (e) 0?arrow_forwardThe three charged particles in Figure P20.11 are at the vertices of an isosceles triangle (where d = 2.00 cm). Taking q = 7.00 C, calculate the electric potential at point A, the midpoint of the base. Figure P20.11arrow_forward
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