Worksheet: 2D Motion in Uniform Electric Fields

In this worksheet, we will practice analyzing the motion of charged objects that move in arbitrary directions through uniform electric fields.

Q1:

A particle has a mass of 3 . 1 0 × 1 0 k g and a charge of 8 . 5 0 × 1 0 C. The particle is moving at a speed of 452 m/s perpendicularly to the uniform electric field when it enters the field, as shown in the diagram. The particle moves 8.62 mm in the direction of the field before it exits it. What is the strength of the electric field?

Q2:

A positively charged particle with a charge of 2.45 µC and a mass of 1 . 2 8 × 1 0 kg moves perpendicularly to a uniform electric field, as shown in the diagram. Find the speed 𝑣 of the particle at the point where it leaves the field. Answer to two significant figures.

Q3:

A particle with a charge of 1.02 µC has a kinetic energy of 0.422 µJ when it enters a region of a uniform electric field. The particle enters the field from below, as shown in the diagram. A short time later, the particle exits the top of the electric field, having meanwhile traveled 115 cm in the direction of the field.

What is the kinetic energy of the particle when it leaves the electric field?

When the particle exits the electric field, is the angle between the particle’s direction of motion and the direction of the field greater than, less than, or equal to the angle between the particle’s direction of motion when it enters the field and the direction of the field?

  • ALess
  • BGreater
  • CEqual

Q4:

A pair of oppositely charged parallel plates separated from each other by a 10 m distance have a potential difference of 20 V across them due to the uniform electric field between them. A positively charged object is propelled into the field perpendicular to its direction, starting from the positively charged plate and crossing the field completely in the time it takes the object to reach the negatively charged plate, which is 0.64 s. The object is retrieved, and the plates are moved so that they are 5.0 m apart. The object is then propelled into the field, and when it crosses between the plates, it is displaced the same distance perpendicular to the direction of the field as the first time it passed between the plates. How much less time is taken for the object to complete its motion if the plates are 5 m apart?

  • A 0.19 s
  • B 0.38 s
  • C 9.4 s
  • D 0.45 s
  • E 6.3 s

Q5:

A particle has a mass of 4 . 6 × 1 0 kg and a charge of 2 . 5 × 1 0 C. The particle is moving diagonally toward a uniform electric field, as shown in the diagram. The particle exits the electric field traveling perpendicularly to it after moving 1.25 mm in the opposite direction to the field.

What is the strength of the electric field?

  • A 4 . 1 × 1 0 N/C
  • B 3 . 6 × 1 0 N/C
  • C 8 . 2 × 1 0 N/C
  • D 6 . 5 × 1 0 N/C
  • E 2 . 9 × 1 0 N/C

What is the power supplied to the particle by the electric field?

Q6:

A particle has a mass of 6 . 2 9 × 1 0 kg and a charge of 10.2 µC. The particle is moving at a speed of 216 m/s perpendicularly to the uniform electric field when it enters the field, as shown in the diagram. What is the speed of the particle in the direction of the field 𝑣 at the point that the particle exits the field?

  • A 19.8 m/s
  • B 164 m/s
  • C 1.65 m/s
  • D 13.4 m/s
  • E 1.98 m/s

Q7:

An object of mass 2.5 kg has a charge of 0.75 C. The object is thrown horizontally into a vertically upward-directed uniform electric field through which it travels for 2.25 m at an average horizontal speed of 15 cm/s. The object descends 5.5 m while traveling through the electric field. Find the electric field strength.

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