Concept explainers
It is shown in Example 24.7 that the potential at a point P a distance a above one end of a uniformly charged rod of length ℓ lying along the x axis is
Use this result to derive an expression for the y component of the electric field at P.
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Chapter 24 Solutions
Physics for Scientists and Engineers
- Three particles with equal positive charges q are at the corners of an equilateral triangle of side a as shown in Figure P24.15. (a) At what point, if any, in the plane of the particles is the electric potential zero? (b) What is the electric potential at the position of one of the particles due to the other two particles in the triangle? Figure P24.15arrow_forwardAt a certain distance from a charged particle, the magnitude of the electric field is 500 V/m and the electric potential is 3.00 kV. (a) What is the distance to the particle? (b) What is the magnitude of the charge?arrow_forwardA CD disk of radius (R = 3.0 cm) is sprayed with a charged paint so that the charge varies continually with radial distance r from the center in the following manner =(6.0C/m)r/R ?. Find the potential at a point 4 cm above the center.arrow_forward
- Given two particles with 2.00-C charges as shown in Figure P20.9 and a particle with charge q = 1.28 1018 C at the origin, (a) what is the net force exerted by the two 2.00-C charges on the test charge q? (b) What is the electric field at the origin due to the two 2.00-C particles? (c) What is the electric potential at the origin due to the two 2.00-C particles? Figure P20.9arrow_forwardGiven two particles with 2.00-C charges as shown in Figure P25.19 and a particle with charge q = 1.28 10-18 C at the origin, (a) what is the net force exerted by the two 2.00-C; charges on the charge q? (b) What is the electric field at the origin due to the two 2.00-C particles? (c) What is the electric potential at the origin due to the two 2.00-C particles?arrow_forwardA uniformly charged filament lies along the x axis between x = a = 1.00 m and x = a + = 3.00 m as shown in Figure P25.66. The total charge on the filament is 1.60 nC. Calculate successive approximations for the electric potential at the origin by modeling the filament as (a) a single charged particle at x = 2.00 m, (b) two 0.800-nC charged particles at x = 1.5 m and x = 2.5 m, and (c) four 0.400-nC charged particles at x = 1.25 m, x = 1.75 m, x = 2.25 m, and x = 2.75 m. (d) Explain how the results compare with the potential given by the exact expression v=klQlln(l+aa)arrow_forward
- A uniform electric field of magnitude 325 V/m is directed in the negative y direction in Figure P20.1. The coordinates of point are (0.200, 0.300) m, and those of point are (0.400, 0.500) m. Calculate the electric potential difference using the dashed-line path. Figure P20.1arrow_forwardA 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 positive point charge q = +2.50 nC is located at x = 1.20 m and a negative charge of 2q = 5.00 nC is located at the origin as in Figure P16.18. (a) Sketch the electric potential versus x for points along the x-axis in the range 1.50 m x 1.50 m. (b) Find a symbolic expression for the potential on the x-axis at an arbitrary point P between the two charges. (c) Find the electric potential at x = 0.600 m. (d) Find the point along the x-axis between the two charges where the electric potential is zero.arrow_forward
- A positive point charge q = +2.50 nC is located at x = 1.20 m and a negative charge of 2q = 5.00 nC is located at the origin as in Figure P16.18. (a) Sketch the electric potential versus x for points along the x-axis in the range 1.50 m x 1.50 m. (b) Find a symbolic expression for the potential on the x-axis at an arbitrary point P between the two charges. (c) Find the electric potential at x = 0.600 m. (d) Find the point along the x-axis between the two charges where the electric potential is zero.arrow_forwardThe naturally occurring charge on the ground on a fine day out in the open country is -1.00nC/m2. (a) What is the electric field relative to ground at a height of 3.00 m? (b) Calculate the electric potential at this height. (C) Sketch electric field and equipotential lines for this scenario.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
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