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If the electrical field intensity E in the region between two parallel plates is 3.0 x 104NC-1. Calculate: (a) The force F on the electron in the region. (b) The acceleration of an electron when acted on the force.

Physics

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Answers

2 parts
a

4.806×10−18 N\text{4.806} \times 10^{-18} \text{ N}

b

5.276×1012 m/s2\text{5.276} \times 10^{12} \text{ m/s}^2

Step-by-step solution

6 steps

Here's how to solve the problem:

Given:
Electric field intensity, E=3.0×10 N C−1E = 3.0 \times 10 \text{ N C}^{-1}
Charge of an electron, qe=1.602×10−19 Cq_e = 1.602 \times 10^{-19} \text{ C}
Mass of an electron, me=9.109×10−31 kgm_e = 9.109 \times 10^{-31} \text{ kg}

Part a· 3 steps

The force FF on the electron in the region.

  1. Use the formula for the force on a charge in an electric field.

    The force FF experienced by a charge qq in an electric field EE is given by:

    F=qEF = qE
  2. Substitute the given values into the formula.

    F=(1.602×10−19 C)×(3.0×10 N C−1)F = (1.602 \times 10^{-19} \text{ C}) \times (3.0 \times 10 \text{ N C}^{-1})
  3. Calculate the force.

    F=4.806×10−18 NF = 4.806 \times 10^{-18} \text{ N}

    The force on the electron is 4.806×10−18 N\boxed{\text{4.806} \times 10^{-18} \text{ N}}.

Part b

5.276×1012 m/s2\text{5.276} \times 10^{12} \text{ m/s}^2

The acceleration of an electron when acted on the force.

  1. Use Newton's second law of motion.

    Newton's second law states that force equals mass times acceleration (F=maF = ma). Therefore, acceleration aa can be found by:

    a=Fmea = \frac{F}{m_e}
  2. Substitute the calculated force and the mass of the electron into the formula.

    a=4.806×10−18 N9.109×10−31 kga = \frac{4.806 \times 10^{-18} \text{ N}}{9.109 \times 10^{-31} \text{ kg}}
  3. Calculate the acceleration.

    a≈0.5276×1013 m/s2a \approx 0.5276 \times 10^{13} \text{ m/s}^2 a≈5.276×1012 m/s2a \approx 5.276 \times 10^{12} \text{ m/s}^2

    The acceleration of the electron is approximately 5.276×1012 m/s2\boxed{\text{5.276} \times 10^{12} \text{ m/s}^2}.

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