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

ID: 1413099 • Letter: A

Question

A very long uniform line of charge, has a charge per unit length lambda = -1.50 nC and lies along the z-axis. A point charge q =3.00 nC 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, z =0.00 m (use I - hat, J - hat, k - hat 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, R=0.00 m) and point A. A proton (m_p= 1.67 times 10^-27 kg q_p = 1.60 times 10^-19 C) travels from point A to point B. Its speed at point A is V_A = 1.50 times 10^4m/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