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An experiment is set up to investigate the behaviour of electrons in electric fields - Scottish Highers Physics - Question 7 - 2016

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An experiment is set up to investigate the behaviour of electrons in electric fields. (a) Electrons are accelerated from rest between the cathode and the anode by a... show full transcript

Worked Solution & Example Answer:An experiment is set up to investigate the behaviour of electrons in electric fields - Scottish Highers Physics - Question 7 - 2016

Step 1

Calculate the kinetic energy gained by each electron as it reaches the anode.

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Answer

To calculate the kinetic energy (KE) gained by each electron:

The formula for kinetic energy gained is given by: KE=qVKE = qV

Where:

  • qq is the charge of the electron, approximately 1.6×1019 C1.6 \times 10^{-19} \text{ C}.
  • VV is the potential difference, which is 2000 V2000 \text{ V}.

Substituting the values: KE=(1.6×1019)(2000)=3.2×1016 JKE = (1.6 \times 10^{-19})(2000) = 3.2 \times 10^{-16} \text{ J}

Thus, the kinetic energy gained by each electron as it reaches the anode is 3.2×1016 J3.2 \times 10^{-16} \text{ J}.

Step 2

Determine the number of electrons passing between the metal plates in one minute.

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Answer

The number of electrons can be calculated using the formula: Q=ItQ = It Where:

  • QQ is the total charge,
  • II is the current (8.0 mA=0.008 A8.0 \text{ mA} = 0.008 \text{ A}),
  • tt is the time (in seconds, 1 minute=60 s1 \text{ minute} = 60 \text{ s}).

First, we calculate the total charge in one minute: Q=(0.008)(60)=0.48 CQ = (0.008)(60) = 0.48 \text{ C}

Next, we find the number of electrons: The charge of one electron is 1.6×1019 C1.6 \times 10^{-19} \text{ C}, hence: Number of electrons=Qq=0.481.6×1019=3.0×1018\text{Number of electrons} = \frac{Q}{q} = \frac{0.48}{1.6 \times 10^{-19}} = 3.0 \times 10^{18}

Therefore, the number of electrons passing between the metal plates in one minute is approximately 3.0×10183.0 \times 10^{18}.

Step 3

Complete the diagram to show the electric field pattern between the two metal plates.

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Answer

To represent the electric field pattern:

  • Draw straight lines with arrows pointing downwards between the two metal plates, indicating the direction of the electric field.
  • Ensure that the spacing between the lines is uniform, showing an approximately equal field strength.
  • The lines should start and finish on the plates, maintaining right angles to the plates.

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