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Fields · Question 9

Fields · Original GioPhysics question with a detailed, mark-by-mark answer guide.

Demand
demanding
Marks
12
Topics
2
Answer
Complete
An electron accelerated through a potential difference, then entering a magnetic fieldcathodeanode+500 Velectronuniform magnetic field, B = 2.5 mT, into the page
Figure 5Side view of the arrangement. At the left a cathode plate marked − faces an anode plate marked + which has a small hole in it at the level of the beam; below, the two plates are joined by wires through a cell labelled 500 V, whose positive terminal is connected to the anode. Arrows show an electron leaving the cathode, passing through the hole in the anode and travelling on to the right, where it crosses into a large rectangular region drawn with a dashed boundary and filled with crosses, labelled 'uniform magnetic field, B = 2.5 mT, into the page'. Inside that region the electron's path is drawn as an arc that curves steadily downwards away from its original straight line.
structured12 marks

An electron is accelerated from rest through a potential difference of 500 V and then enters a region of uniform magnetic field of magnitude 2.5 mT, travelling perpendicular to the field. The mass of an electron is 9.11 × 10⁻³¹ kg and its charge has magnitude 1.60 × 10⁻¹⁹ C.

  1. (a)

    Determine Determine the speed of the electron as it enters the magnetic field.

    3 marks
  2. (b)

    Determine Determine the radius of the circular path followed by the electron in the field.

    3 marks
  3. (c)

    Explain Explain why the speed of the electron is unchanged while it moves within the magnetic field, even though its velocity is changing continuously.

    3 marks
  4. (d)

    Compare A uniform electric field is now applied in the same region instead of the magnetic field, perpendicular to the electron's initial velocity. Compare the resulting path and the resulting speed with those in the magnetic field.

    3 marks
Ready to self-mark?Reveal the detailed answer guide
Answer overviewKey answer: The gained electric potential energy becomes kinetic energy, so eV = ½mv². v = √(2 × 1.60 × 10⁻¹⁹ × 500 / 9.11 × 10⁻³¹) v = 1.33 × 10⁷ m s⁻¹
01

(a)

3 marks

Determine Determine the speed of the electron as it enters the magnetic field.

How to approach it

List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.

  1. 1

    The gained electric potential energy becomes kinetic energy, so eV = ½mv².

  2. 2

    v = √(2 × 1.60 × 10⁻¹⁹ × 500 / 9.11 × 10⁻³¹)

  3. 3

    v = 1.33 × 10⁷ m s⁻¹

02

(b)

3 marks

Determine Determine the radius of the circular path followed by the electron in the field.

How to approach it

List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.

  1. 1

    the magnetic force provides the centripetal force: evB = mv²/r

  2. 2

    r = mv/(eB) = 9.11 × 10⁻³¹ × 1.33 × 10⁷ / (1.60 × 10⁻¹⁹ × 2.5 × 10⁻³)

  3. 3

    r = 3.0 × 10⁻² m

03

(c)

3 marks

Explain Explain why the speed of the electron is unchanged while it moves within the magnetic field, even though its velocity is changing continuously.

How to approach it

State the outcome first, then link cause to effect with the relevant physical principle. Each link in the reasoning should be explicit enough to earn its own marking point.

  1. 1

    the magnetic force is always perpendicular to the velocity

  2. 2

    so it has no component along the direction of motion and does no work on the electron

  3. 3

    the kinetic energy is therefore constant, and only the direction of the velocity changes

04

(d)

3 marks

Compare A uniform electric field is now applied in the same region instead of the magnetic field, perpendicular to the electron's initial velocity. Compare the resulting path and the resulting speed with those in the magnetic field.

How to approach it

Identify what the question is testing, organise the response into distinct mark-earning points, and make every conclusion traceable to a physical principle or to the evidence supplied.

  1. 1

    in the electric field the force is constant in magnitude and direction, so the path is parabolic rather than circular

  2. 2

    the force has a component along the velocity once the electron has been deflected, so it does work and the speed increases

  3. 3

    in the magnetic field the force turns with the velocity, keeping the path circular and the speed constant

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