Two parallel copper plates are 5.0 cm apart and have a uniform electric field, E = 12000 N/C, between them. An electron is released from the negative plate at the same time that a proton is...

Two parallel copper plates are 5.0 cm apart and have a uniform electric field, E = 12000 N/C, between them. An electron is released from the negative plate at the same time that a proton is released from the positive plate. Which particle reaches the attracting plate first? How much sooner does it arrive?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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Two large parallel copper plates are placed 5.0 cm apart and there is a uniform electric field of E = 12000 N/C, between them. An electron is released from the negative plate at the same time that a proton is released from the positive plate.

The magnitude of electrical charge on both the electron as well as the proton is the same. The electron has a negative charge of 1.602*10^-19 C and the proton has a positive charge of 1.602*10^-19 C. The mass of a proton is 1.762*10^-27 kg and the mass of an electron is 9.109*10^-31 kg.

As the force acting on both the particles is the same but the mass of an electron is approximately 1/1000 the mass of a proton it is accelerated by a larger extent and will reach the oppositely charged plate faster.

The time taken by the electron to reach the oppositely charged plate is t given by 5*10^-100 = (1/2)*(12000*1.602*10^-19)/9.109*10^-31*t^2

=> t = 6.88*10^-9 s.

The time taken by the proton to reach the plate is t given by 5*10^-100 = (1/2)*(12000*1.602*10^-19)/1.762*10^-27*t^2

=> t = 3.02*10^-7 s

The time taken by the electron to reach the oppositely charged plate is 6.88*10^-9 s and that taken by the proton is 3.02*10^-7 s

Sources:

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