Worksheet: Uniform Electric Fields

In this worksheet, we will practice determining the change in potential energy of charged objects that move parallel to uniform electric fields.

Q1:

A positively charged particle moves at a constant speed between the point 𝐴 and the point 𝐡 where it enters a uniform electric field. Assume that gravitational and drag forces on the particle are negligible.

Which of the sections of the particle’s trajectory can be consistent with the net work done on the particle being zero?

  • A 𝐡 to 𝐷 only
  • B 𝐡 to 𝐢 only
  • C 𝐴 to 𝐡 only
  • D 𝐴 to 𝐡 and 𝐡 to 𝐢
  • E 𝐴 to 𝐡 and 𝐡 to 𝐷

Which of the sections of the particle’s trajectory can be consistent with the net work done by the particle being zero?

  • A 𝐴 to 𝐡 only
  • B 𝐡 to 𝐢 only
  • C 𝐡 to 𝐷 only
  • D 𝐴 to 𝐡 and 𝐡 to 𝐷
  • E 𝐴 to 𝐡 and 𝐡 to 𝐢

Q2:

A positively charged object moves 13 cm inside and parallel to a uniform electric field with a strength of 1.28 mN/C, as shown in the diagram. What is the potential difference between the object’s initial and final positions? Answer to two significant figures.

Q3:

Which of the following formulas correctly relates the electric potential difference between two points in a uniform electric field to the electric field strength, where 𝑉 is the electric potential difference, π‘ž is the charge of a particle in the field, 𝑑 is the distance between the points, π‘˜ is the Coulomb constant, and 𝐸 is the electric field strength?

  • A 𝑉 = 𝐸 𝑑
  • B 𝑉 = 𝐸 π‘ž 𝑑
  • C 𝑉 = π‘˜ π‘ž 𝑑
  • D 𝑉 = 𝐸 𝑑
  • E 𝑉 = 𝐸 π‘ž 𝑑

Q4:

A pair of parallel plates produce a uniform electric field between them. The electric field has a strength of 45 mN/C. A positively charged particle moves directly from the positively charged plate toward the negatively charged plate, as shown in the diagram.

Find the potential difference between the positive plate and point 𝐴 .

Find the potential difference between the negative plate and point 𝐴 .

Find the potential difference between the positive plate and point 𝐡 .

Find the potential difference between the negative plate and point 𝐡 .

Find the potential difference between the positive plate and point 𝐢 .

Find the potential difference between the negative plate and point 𝐢 .

Find the potential difference between the plates.

Q5:

A pair of parallel plates produces a uniform electric field between them. The electric field has a strength of 745 mN/C. A particle with a charge of 16.2 mC moves in the field as shown in the diagram.

What is the potential difference between the particle's initial and final position?

How much work is done on the particle while it is moving in the direction of the field?

How much work is done by the particle while it is moving in the direction opposite to the field?

Q6:

A positively charged particle has a mass in kilograms equal to one-hundredth of its charge in coulombs. The particle moves parallel to a uniform electric field, as shown in the diagram.

What is the potential difference between the particle’s initial and final positions?

How much does the particle’s speed increase due to the work done on it by the electric field?

Q7:

A pair of parallel plates produce a uniform electric field between them. The electric field has a strength of 225 mN/C. A positively charged particle moves in the field toward the negatively charged plate, as shown in the diagram. What is the potential difference between the particle's initial and final position? Answer to two significant figures.

Q8:

The diagrams (a), (b), and (c) show arrangements of pairs of positive and negative charges. The charges in the pairs are separated by multiples of the distance 𝑑 and the pairs are separated by the distance 𝐿 , where 𝐿 is much greater than 𝑑 . Diagram (d) shows the change in the net electric field strength 𝐸 of each of the pairs along 𝐿 at different distances and also shows the average strength of 𝐸 along 𝐿 for that pair, which is shown in detail in diagram (e).

Fill in the blanks: The electric field along 𝐿 between pairs of opposite sign charges has the strength near either of the pairs and the strength halfway between the pairs.

  • Agreatest, smallest
  • Bleast, greatest

Fill in the blanks: The average strength of the electric field along 𝐿 between pairs of opposite sign charges is much closer to its strength than its strength.

  • Asmallest, greatest
  • Bgreatest, least

Fill in the blanks: In a uniform electric field, the average field strength is the maximum field strength and the minimum field strength is the average field strength.

  • Aequal to, less than
  • Bgreater than, equal to
  • Cequal to, equal to
  • Dless than, greater than
  • Egreater than, less than

As the total charge of a pair of opposite sign charges is kept constant while that charge is distributed over a greater distance perpendicular to 𝐿 , does the difference between the maximum strength of the electric field produced along 𝐿 and the average electric field strength along 𝐿 increase, remain constant, or decrease?

  • ARemain constant
  • BIncrease
  • CDecrease

Q9:

The diagrams show the electric field lines produced by horizontal lines of negatively charged objects consisting of different numbers of charged objects with different separations between them. The length of a line of charges is 𝐿 and the distance between the charges is 𝑑 .

Complete the following statements about the reasons for the shape of the resultant electric fields of these charges:

The the distance 𝑑 between adjacent charges, the closer the field lines near the center of the line of charges are to being to the line. The field lines that pass through a line of length 𝐿 , parallel to the line of charge, more closely approximate a field the nearer that the parallel line is to the line of charge at distances greater than from the line of charge.

  • Asmaller, perpendicular, uniform, 𝐿
  • Bsmaller, perpendicular, uniform, 𝑑
  • Csmaller, perpendicular, radial, 𝑑
  • Dsmaller, parallel, uniform, 𝑑
  • Elarger, perpendicular, uniform, 𝑑

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