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Show that the maximum magnitude Emax of the electric field along the axis of a uniformly charged ring occurs at
Figure 23.3 (Example 23.2) A uniformly charged ring of radius c. (a) The field at P on the x axis due to an element of charge dq. (b) The perpendicular component of the field at P due to segment 1 is canceled by the perpendicular component due to segment 2.
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Chapter 23 Solutions
Bundle: Physics for Scientists and Engineers, Volume 2, Loose-leaf Version, 10th + WebAssign Printed Access Card for Serway/Jewett's Physics for Scientists and Engineers, 10th, Multi-Term
- When a piece of paper is held with one face perpendicular to a uniform electric field, the flux through it is 32 Nm(^2)/C. When the paper is turned 40 degrees with respect to the field, the flux through it is: a. 25 Nm(^2)/C b. 23 Nm(^2)/C c. 27 Nm(^2)/C d. 29 Nm(^2)/Carrow_forwardWhat must the charge (sign and magnitude) of a 3.45 gg particle be for it to remain stationary when placed in a downward-directed electric field of magnitude 590 N/C?arrow_forwardA proton is initially moving horizontally at v0= 3x106 m/s when it enters a uniform electric field of 5.6 N/C directed vertically down. What are the horizontal and vertical components of its velocity 2.0 μs after entering the electric field?arrow_forward
- What is the electric field intensity 2 m from the surface of the rod, 20cm in diameter, having a linear charge density of +8 nC/m2? [ A = 4πR2; r = 2 m + 0.2 m = 2.2 m] 68.50 N/C 52.76 N/C 71.93 N/C 45.90 N/Carrow_forwardThe electric field is zero everywhere except in the region 0≤x≤4.00 cm, where there is a uniform electric field of 110 N/C in the +y direction. A proton is moving in the +x direction with a speed of v = 1.00×10^6 m/s. When the proton passes through the region 0≤x≤4.00 cm, the electric field exerts a force on it. 1)When the x coordinate of the proton’s position is 4.00 cm, what is the x component of its velocity? (Express your answer to three significant figures.) 2)When the x coordinate of the proton’s position is 4.00 cm, what is the y component of its velocity?(Express your answer to three significant figures.) 3)When the x coordinate of its position equals 10.0 cm, what is the y component of its velocity? (Express your answer to three significant figures.)arrow_forwardA cylindrical metal rod of radius 7.7 cm and length 291 cm is uniformly charged. The mag- nitude of the electric field at a point located at distance 22 cm from its axis is 52400 N/C. What is the net charge on the metal rod? The Coulomb constant is 8.99 x 109 Nm²/C². 1. 1.36737 x 10-6 2. 2.62325 x 10 -6 3. 2.17308 x 10-6 4. 1.86577 x 10-6 5. 1.79526 x 10-6 6. 1.89852 x 10-6 7. 2.80164 x 10-6 8. 2.13835 x 10-6 9. 2.31838 x 107 10. 1.3007 x 10-6 Answer in units of C.arrow_forward
- 9. A 40.0 cm diameter loop is rotated to the position where the greatest flux is obtained in a uniform electric field. At this location, the flux is measured as 5 .20x10 ^ 5 N.m ^ 2 / C. Find the magnitude of the electric field. 8.14x105N / C2.14x106 NC5.44x106 N / C6.14x106N / C4.14x106N / Carrow_forwardThe electric field is zero everywhere except in the region 0≤x≤4.00 cm, where there is a uniform electric field of 110 N/C in the +y direction. A proton is moving in the +x direction with a speed of v = 1.00×10^6 m/s. When the proton passes through the region 0≤x≤4.00 cm, the electric field exerts a force on it. 1)When the x coordinate of the proton’s position is 4.00 cm, what is the y component of its velocity?(Express your answer to three significant figures.)arrow_forwardA proton is initially moving horizontally at v0= 3 X 106 m/s when it enters a uniform electric field of 5.6 N/C directed vertically down. What are the horizontal and vertical components of its velocity 2.0 μs after entering the electric field?arrow_forward
- A proton is placed in an electric field of intensity 700 N/C .What are the magnitude and direction of the acceleration of this proton due to this field?(mproton=1.67×10-27 kg ,qe =1.60×10-19C) Select one: a. 6.71×109m/s2 opposite to the electric field b. 6.71×1010m/s2 opposite to the electric field c. 6.71×1010m/s2 in the direction of the electric field d. 67.1×1010m/s2 opposite to the electric field e. 67.1×1010m/s2 in the direction of the electric fieldarrow_forwardA solid conducting sphere of radius 2.00 cm has a charge of 8.82 µC. A conducting spherical shell of inner radius 4.00 cm and outer radius 5.00 cm is concentric with the solid sphere and has a charge of −2.62 µC. Find the electric field at the following radii from the center of this charge configuration. (a) r = 1.00 cm(b) r = 3.00 cm(c) r = 4.50 cm(d) r = 7.00 cmarrow_forwardA solid insulating sphere of radius a = 5.00 cm carries a net positive charge of Q = 3.00 C uniformly distributed throughout its volume. Concentric with this sphere is a conducting spherical shell with inner radius b = 10.0 cm and outer radius c = 15.0 cm as shown in Figure P24.54, having net charge q = 1.00 C Prepare a graph of the magnitude of the electric field due to this configuration versus r for O r 25.0 cm.arrow_forward
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