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Worksheet: Force on a Charge Due to an Electric Field

Q1:

The electric field strength in a particular thundercloud is 2 . 0 × 1 0 5 N/C. What is the magnitude of the acceleration of an electron in this field?

  • A 3 . 1 × 1 0 1 6 m/s2
  • B 2 . 8 × 1 0 1 6 m/s2
  • C 3 . 9 × 1 0 1 6 m/s2
  • D 3 . 5 × 1 0 1 6 m/s2
  • E 4 . 3 × 1 0 1 6 m/s2

Q2:

What is the magnitude of an electric field that supports the weight of a free electron near the surface of Earth?

  • A 2 . 5 1 × 1 0 N/C
  • B 8 . 3 3 × 1 0 N/C
  • C 8 . 7 4 × 1 0 N/C
  • D 5 . 5 8 × 1 0 N/C
  • E 1 . 0 4 × 1 0 N/C

Q3:

What is the electric field at a point where the force on a 2 . 0 × 1 0 6 C charge is ( 4 . 0 6 . 0 ) × 1 0 i j 6 N/C?

  • A ( 3 . 0 + 2 . 0 ) i j N
  • B ( 1 . 0 + 3 . 0 ) i j N
  • C ( 2 . 0 + 1 . 5 ) i j N
  • D ( 2 . 0 + 3 . 0 ) i j N
  • E ( 2 . 0 3 . 0 ) i j N

Q4:

A particle with a charge of + 2 . 0 × 1 0 8 C is acted on by a force of magnitude 4 . 0 × 1 0 6 N when it is placed in a particular point in an electric field.

What is the electric field magnitude at the point?

  • A 1 . 4 × 1 0 2 N/C
  • B 1 . 0 × 1 0 2 N/C
  • C 1 . 7 × 1 0 2 N/C
  • D 2 . 0 × 1 0 2 N/C
  • E 2 . 3 × 1 0 2 N/C

If a particle with a charge of 1 . 0 × 1 0 8 C is instead placed at the point, what force acts on the particle?

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

Q5:

At a point 𝑃 near Earth’s surface, the direction of Earth’s electric field is vertically downward and its magnitude is 160 N/C. A small dust particle with a mass of 6 . 0 × 1 0 1 5 g is located at 𝑃 . If the dust particle carries an electric charge that is equal to that of a single electron, what is the magnitude of the net acceleration of the particle?

Q6:

An electron is suspended at rest in the air just above the surface of Earth by an electric field. What is the magnitude of the electric field at this point?

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

Q7:

A small piece of cork with a mass of 9.00 g is given a charge of 1 2 . 0 × 1 0 7 C. What is the minimum magnitude of the applied electric field required to suspend the cork at rest in the air just above Earth’s surface under the combined electric and gravitational forces of the applied electric field and Earth’s gravitational field?

  • A 5 . 3 6 × 1 0 4 N/C
  • B 1 2 . 3 × 1 0 4 N/C
  • C 9 2 . 3 × 1 0 4 N/C
  • D 7 . 3 5 × 1 0 4 N/C
  • E 4 5 . 6 × 1 0 4 N/C

Q8:

A proton and an electron both move in the electric field E i = 2 0 0 / N C .

What is the force on the proton?

  • A 2 . 5 × 1 0 1 7 i N
  • B 2 . 1 × 1 0 1 7 i N
  • C 2 . 8 × 1 0 1 7 i N
  • D 3 . 2 × 1 0 1 7 i N
  • E 3 . 5 × 1 0 1 7 i N

What is the acceleration of the proton?

  • A 1 . 9 × 1 0 1 0 i m/s2
  • B 2 . 7 × 1 0 1 0 i m/s2
  • C 2 . 3 × 1 0 1 0 i m/s2
  • D 1 . 6 × 1 0 1 0 i m/s2
  • E 3 . 2 × 1 0 1 0 i m/s2

What is the force on the electron?

  • A 3 . 9 × 1 0 1 7 i N
  • B 3 . 9 × 1 0 1 7 i N
  • C 3 . 2 × 1 0 1 7 i N
  • D 1 . 3 × 1 0 1 7 i N
  • E 1 . 3 × 1 0 1 7 i N

What is the acceleration of the electron?

  • A 3 . 5 × 1 0 1 3 i m/s2
  • B 3 . 1 × 1 0 1 3 i m/s2
  • C 1 . 5 × 1 0 1 3 i m/s2
  • D 3 . 1 × 1 0 1 3 i m/s2
  • E 1 . 5 × 1 0 1 3 i m/s2

Q9:

A proton moving horizontally at 1 . 3 × 1 0 7 m/s enters a region containing a uniform electric field produced by two charged plates. The electric field is modeled as being of uniform strength over the 12.0 cm length of the plates, as shown in the diagram. The magnitude of the electric field in the region is 3 . 5 × 1 0 5 N/C. By what distance 𝑑 is the proton deflected downward in its passage through the region containing the field?

  • A 9 8 0 × 1 0 3 m
  • B 3 . 6 × 1 0 3 m
  • C 7 8 × 1 0 3 m
  • D 1 . 4 × 1 0 3 m
  • E 9 5 × 1 0 3 m

Q10:

An electron has a velocity of 5 . 0 0 × 1 0 6 m/s when it reaches a point 𝑃 , which is the point at which the electron enters a uniform electric field of magnitude 2 . 0 0 × 1 0 5 N/C, directed oppositely to the initial velocity of the electron. The electron is decelerated by the field until it comes instantaneously to rest and is then accelerated in the opposite direction to its initial velocity.

How much time passes between the electron reaching the point 𝑃 and coming instantaneously to rest?

  • A 1 . 1 4 × 1 0 9 s
  • B 4 . 4 2 × 1 0 9 s
  • C 6 . 2 1 × 1 0 1 0 s
  • D 1 . 4 2 × 1 0 1 0 s
  • E 4 . 0 5 × 1 0 9 s

What is the velocity of the electron when it returns to the point 𝑃 ?

  • A 5 . 0 0 × 1 0 6 m/s
  • B 3 . 4 1 × 1 0 6 m/s
  • C 2 . 5 0 × 1 0 6 m/s
  • D 2 . 2 0 × 1 0 6 m/s
  • E 5 . 7 5 × 1 0 6 m/s

Q11:

Two charged conductive spheres of radii 𝑅 = 2 . 5 1 cm and 𝑅 2 , respectively, are connected by a wire, as shown in the diagram. A value of 𝑅 2 is chosen that will result in an electric field of magnitude 2 . 3 × 1 0 6 V/m at the surface of the smaller sphere when the larger sphere is placed in an electric field of magnitude 302 V/m. Find 𝑅 2 .

  • A 4 . 2 × 1 0 3 cm
  • B 2 . 3 × 1 0 3 cm
  • C 5 . 2 × 1 0 3 cm
  • D 3 . 3 × 1 0 3 cm
  • E 1 . 5 × 1 0 3 cm

Q12:

An electric dipole consists of two particles separated vertically by 10.0 cm, each having a charge of 9.0 µC.

What is the dipole moment of this pair of particles?

  • A 4 . 2 × 1 0 6 C⋅m
  • B 3 . 6 × 1 0 6 C⋅m
  • C 6 . 3 × 1 0 6 C⋅m
  • D 1 . 8 × 1 0 6 C⋅m
  • E 7 4 × 1 0 6 C⋅m

What is the magnitude of the torque on the dipole when it is placed in a horizontally aligned electric field of magnitude 6 . 5 × 1 0 5 N/C?

What is the magnitude of the torque on the dipole when it is placed in a vertically aligned electric field of magnitude 6 . 5 × 1 0 5 N/C?

Q13:

A spherical water droplet of radius 25 μm carries an excess 250 electrons. What magnitude of vertical electric field is needed to balance the gravitational force on the droplet at the surface of the earth?

  • A 2 . 3 × 1 0 7 N/C
  • B 1 . 9 × 1 0 7 N/C
  • C 2 . 6 × 1 0 7 N/C
  • D 1 . 6 × 1 0 7 N/C
  • E 3 . 0 × 1 0 7 N/C

Q14:

An electrostatic paint sprayer has a 0.400 m diameter metal sphere at a potential of 23.4 kV that repels paint droplets onto a grounded object.

What charge is on the sphere?

A drop of paint of mass 1.00 mg moves from a point negligibly far from the surface of the charged sphere and toward the grounded object. The drop has a speed of 10.0 m/s when it arrives at the grounded object. Find the charge carried by the paint drop. Assume that the change in the potential of the sphere across the distance from its surface to the grounded object is negligible, and assume that any acceleration of the drop due to gravity is negligible.

Q15:

An oxygen nucleus has a charge of 1 . 2 8 × 1 0 1 8 C. The nucleus is placed 1 . 0 0 × 1 0 1 0 m away from a second oxygen nucleus.

What is the magnitude of the electric field from one oxygen nucleus at the position of the other nucleus?

  • A 1 . 2 7 × 1 0 1 2 N/C
  • B 1 . 2 1 × 1 0 1 2 N/C
  • C 1 . 3 3 × 1 0 1 2 N/C
  • D 1 . 1 5 × 1 0 1 2 N/C
  • E 1 . 4 0 × 1 0 1 2 N/C

What is the magnitude of the electric force that one oxygen nucleus exerts on the other nucleus?

  • A 1 . 4 7 × 1 0 6 N
  • B 1 . 3 3 × 1 0 1 2 N
  • C 1 . 2 7 × 1 0 1 2 N
  • D 1 . 2 1 × 1 0 1 2 N
  • E 1 . 4 0 × 1 0 1 2 N