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Lesson_2.5_Homework_and_Solutions

# Lesson_2.5_Homework_and_Solutions - Lesson 2.5 Homework...

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Lesson 2.5 Homework Solutions 1. In the Bohr model of the hydrogen atom, the electron orbit closest to the nucleus has a radius of 5.29 × 10 -11 m. (i) Find the electric potential of the proton at the position of the electron. (ii) Calculate the electric potential energy of the electron at this position. 9 9 11 1 19 1 9 10 1.602 10 27.3 5. 4.4 10 29 10 2.73 1.602 10 kq V V U J r Vdq - - - - × × × = = = × = - - × = - × × = 2. A uniform electric field of 2 kN.C -1 is in the x direction. A positive charge q = 3 μ C is released from rest at the origin. (i) What is the potential difference V(4 m) – V(0)?. (ii) What is the change in potential energy of the charge from x = 0 to x = 4 m? (iii) What is the kinetic energy of the charge when it is at x = 4 m. (iv) find the potential V(x) if (a) V(0) = 0, (b) V(1) = 0. (i) v = - E x = - 2.0 × 10 3 × 4 = - 8.0 kV (ii) The change in potential energy U is a measure of the work done on the charge. Work done = Charge × potential difference. U = q V = 3 × 10 -6 × (-8 × 10 3 ) = -24 mJ. (iii) Loss in potential energy = gain in kinetic energy K = 24 mJ (iv) (a) (2000 ) 2000 V Edx d x c x = - - = = - (b) V(0) = 0 gives c = 0 V(x) = -2000x (c) V(1) = 0 gives 0 = 2000 + c, or c = -2000 V = -(2000x – 2000) = 2000 – 2000x 3. A constant electric field E = 5.6 × 10 3 N.C -1 i exists in a region of space. What is the potential difference between the initial point x = 0 and the final point x = 5m?

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