Worksheet: Electric Field Equipotential Lines

In this worksheet, we will practice identifying equipotential lines of electric fields and their relations to changes of energy of particles in such fields.

Q1:

The diagram shows a pair of charged plates, one of which is regularly shaped and the other is irregularly shaped and has a nonuniform charge. Some areas in the electric field between the plates are uniform and other areas are nonuniform. Which of the following sets of points are at the same potential as each other?

  • A𝑉=π‘‰οŒ½οŒΏ and 𝑉=𝑉
  • B𝑉=𝑉=𝑉=π‘‰οŒΊοŒΌοŒ½οŒΎ
  • C𝑉=𝑉=π‘‰οŒ½οŒΏο€ and 𝑉=𝑉=𝑉=π‘‰οŒΎο‚οƒο…
  • D𝑉=π‘‰οŒΊοŒ»

Q2:

Two surfaces, with equal uniformly distributed total charge, are positioned parallel to each other. The center of one surface is positioned at a greater distance from the surface it faces, as shown in the diagram. Four lines are shown, and the ends of each line intersect the points π‘Ž and 𝑏. Which of the lines could be an equipotential line of the electric field between the surfaces?

  • ALine I
  • BLine III
  • CLine II
  • DLine IV

Q3:

An electron moves along the dashed path shown in the diagram of the electric field equipotential lines of two equal magnitude charges with opposite signs.

Is the electron’s initial kinetic energy zero or nonzero?

  • ANonzero
  • BZero

Does the absolute electric potential change along the path traveled by the electron?

  • AYes
  • BNo

Does the electric potential energy change along the path traveled by the electron?

  • AYes
  • BNo

Does the electron’s kinetic energy change as it travels along the path that it follows?

  • ANo
  • BYes

Q4:

Two oppositely charged surfaces, with equal uniformly distributed total charge, are positioned parallel to each other. The center of the positively charged surface is positioned at a greater distance from the negatively charged surface, as shown in the diagram. Four lines are shown, and the ends of each line intersect the points π‘Ž and 𝑏. Which of the lines could be an equipotential line of the electric field between the surfaces?

  • ALine I
  • BLine IV
  • CLine II
  • DLine III

Q5:

An initially stationary electron moves along the path between the points 𝐴 and 𝐡 shown in the diagram of the electric field equipotential lines of two equal-magnitude charges with opposite signs. The electron is nearer to the negative charge.

Is the magnitude of the absolute electric potential at point 𝐡 less than, equal to, or greater than at point 𝐴?

  • AEqual to
  • BGreater than
  • CLess than

Is the electric potential energy at point 𝐡 greater than, equal to, or less than at point 𝐴?

  • ALess than
  • BEqual to
  • CGreater than

Is the electron’s kinetic energy at point 𝐡 less than, equal to, or greater than at point 𝐴?

  • AGreater than
  • BEqual to
  • CLess than

Q6:

An initially stationary electron moves along the path between the points 𝐴 and 𝐡 shown in the diagram of the electric field equipotential lines of two equal negative charges.

Is the magnitude of the absolute electric potential at point 𝐡 less than, equal to, or greater than at point 𝐴?

  • AGreater than
  • BLess than
  • CEqual to

Is the electric potential energy at point 𝐡 greater than, equal to, or less than at point 𝐴?

  • ALess than
  • BGreater than
  • CEqual to

Is the electron’s kinetic energy at point 𝐡 less than, equal to, or greater than at point 𝐴?

  • ALess than
  • BEqual to
  • CGreater than

Q7:

An electron moves along the path between the points A and B shown in the diagram of the electric field equipotential lines of two equal-magnitude charges with opposite signs. Point A is at the midpoint between the two charges. The electron has no horizontal velocity component.

At point A, is the magnitude of the absolute electric potential zero or nonzero?

  • ANonzero
  • BZero

Does the electric potential energy increase, decrease, or remain constant as the electron moves from A to B?

  • AIncreases
  • BRemains constant
  • CDecreases

Is the magnitude of the absolute electric potential at point B less than, equal to, or greater than at point A?

  • ALess than
  • BEqual to
  • CGreater than

Is the electron’s kinetic energy at point B less than, equal to, or greater than at point A?

  • AEqual to
  • BGreater than
  • CLess than

Q8:

An initially stationary electron moves along the path between the points A and B shown in the diagram of the electric field equipotential lines of two equal-magnitude charges with opposite signs. The electron is nearer to the negative charge. Point B is at the midpoint between the two charges.

Is the magnitude of the absolute electric potential at point B less than, equal to, or greater than at point A?

  • AEqual to
  • BLess than
  • CGreater than

Is the electric potential energy at point B greater than, equal to, or less than at point A?

  • AGreater than
  • BLess than
  • CEqual to

Is the electron’s kinetic energy at point B less than, equal to, or greater than at point A?

  • ALess than
  • BGreater than
  • CEqual to

Q9:

The two charged objects shown in the diagram have charges of π‘žοŠ§ and π‘žοŠ¨ respectively. Lines of equal absolute electric potential around the objects are shown.

Do the charges π‘žοŠ§ and π‘žοŠ¨ have like signs or opposite signs?

  • ALike signs
  • BOpposite signs

Which of the following statements about the magnitudes of charges π‘žοŠ§ and π‘žοŠ¨ is correct?

  • Aπ‘ž=π‘žοŠ§οŠ¨
  • Bπ‘ž<π‘žοŠ§οŠ¨
  • Cπ‘ž>π‘žοŠ§οŠ¨

Q10:

The two charged objects shown in the diagram have charges of π‘žοŠ§ and π‘žοŠ¨ respectively. Lines of equal absolute electric potential around the objects are shown.

Do the charges π‘žοŠ§ and π‘žοŠ¨ have like signs or opposite signs?

  • AOpposite signs
  • BLike signs

Which of the following statements about the magnitudes of charges π‘žοŠ§ and π‘žοŠ¨ is correct?

  • Aπ‘ž=π‘žοŠ§οŠ¨
  • Bπ‘ž<π‘žοŠ§οŠ¨
  • Cπ‘ž>π‘žοŠ§οŠ¨

Q11:

An initially stationary electron moves along the path between the points A and B shown in the diagram of the electric field equipotential lines of two equal negative charges. Point B is at the midpoint between the two charges.

Is the magnitude of the absolute electric potential at point B less than, equal to, or greater than at point A?

  • AEqual to
  • BLess than
  • CGreater than

Is the electric potential energy at point B greater than, equal to, or less than at point A?

  • AEqual to
  • BLess than
  • CGreater than

Is the electron’s kinetic energy at point B less than, equal to, or greater than at point A?

  • AGreater than
  • BLess than
  • CEqual to

Q12:

An electron moves along the path between the points A and B shown in the diagram of the electric field equipotential lines of two equal positive charges.

At point A, is the electron’s kinetic energy zero or nonzero?

  • AZero
  • BNonzero

Is the magnitude of the absolute electric potential at point B less than, equal to, or greater than at point A?

  • AGreater than
  • BLess than
  • CEqual to

Is the electric potential energy change from point A to point B zero or nonzero?

  • ANonzero
  • BZero

Q13:

An electron e moves along the solid path shown in the diagram of the equipotential lines of the electric field of two objects with charges of equal magnitude and opposite signs. The electron is closer to the positively charged object. Another electron e later moves along the dashed path.

Which of the following statements about the kinetic energy of the electrons is correct?

  • AKKee=
  • BKKee<
  • CKKee>

Q14:

An electron e moves along the path between points A and B shown in the diagram of the electric field equipotential lines of two equal positive charges. Another electron e later moves along the path between point A and point C. Which of the following statements about the initial kinetic energy of the electrons is correct? 𝐸 is the kinetic energy of the first electron, and 𝐸 is the kinetic energy of the second electron.

  • A𝐸>𝐸
  • B𝐸<𝐸
  • C𝐸=𝐸

Q15:

Two parallel plates contain different concentrations of electric charge at different points along their lengths, so the electric potential on a plate changes continuously along its length. The plates are at a distance 𝑑 from each other, perpendicular to their lengths, as shown in the diagram. Points opposite to each other on the plates have a potential difference Δ𝑉 between them. The potential difference Δ𝑉 is the same potential difference as the one between two points on a plate that are separated by the distance 𝑑 along the plate. The potential difference Δ𝑉 is 24 V and the distance 𝑑 is 1.5 m.

At what angle from a line perpendicular to the surface of the plates is the direction of the electric field between the plates?

What is the strength of the electric field between the plates in the direction of the field?

What is the strength of the electric field between the plates in the direction perpendicular to the plates?

Q16:

An electron moves along the path between the points A and B shown in the diagram of the electric field equipotential lines of two equal negative charges. Point A is at the midpoint between the two charges.

At point A, is the magnitude of the absolute electric potential zero or nonzero?

  • AZero
  • BNonzero

At point A, is the electric potential energy zero or nonzero?

  • AZero
  • BNonzero

Is the magnitude of the absolute electric potential at point B less than, equal to, or greater than at point A?

  • AEqual to
  • BLess than
  • CGreater than

Is the electron’s kinetic energy at point B less than, equal to, or greater than at point A?

  • AEqual to
  • BLess than
  • CGreater than

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