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A very long uniform line of charge, has a charge per unit length lambda = -1.50

ID: 1413094 • Letter: A

Question

A very long uniform line of charge, has a charge per unit length lambda = -1.50 mC and lies along the z-axis. A point charge q=3.00 mC is located on the y-axis at y=2.50 m. Find the net electric field at a point A, with coordinates x=2.00 m, y=1.50 m, r=0.00 m (use i bar, j bar, k bar notation). Find the electric potential difference V_BA = V_B - V_A, between point B (with coordinates x=0.00 m.y=1.50 m, z=0.00 m) and point A. A proton (m_p = 1.67 times 10^-27 kg, q_p = 1.60 times 10^-19C travels from point A to point B, peed at point A is v_A = 150 times 10-^4 m/s. What is its speed at point B?

Explanation / Answer

a) Net electric field = 2 * 8.98 * 109 * 1.50 * 10-9/2.5 - 8.98 * 109 * 3 * 10-9/5

                               =    5.388 N/C

b)   Electric potential difference =   8.98 * 109 * 3 * 10-9 * (1/2.236 - 1/2.5)

                                                = 1.272 V

c)   total energy = 1.6 * 10-19 * 1.272

                           = 2.0352 * 10-19 J

      => speed at point B = sqrt(3.914 * 10-19 * 2/1.67 * 10-27)

                                        = 2.165 * 104 m/sec