Worksheet: Calculating the Net Electrostatic Force from Multiple Charges

In this worksheet, we will practice calculating the net electrostatic force produced by multiple charged particles in a given arrangement.

Q1:

Point charges π‘ž=+50¡C and π‘ž=βˆ’25¡C are placed 1.0 m apart. What is the magnitude of the force on a third charge π‘ž=+20¡C placed midway between and π‘žοŠ§ and π‘žοŠ¨?

Q2:

Two fixed particles, each of charge +5.0Γ—10 C, are 24 cm apart. What magnitude force do they exert on a third particle of charge βˆ’2.5Γ—10 C that is 13 cm from each of them?

Q3:

Two charges +3.00 Β΅C and +12.0 Β΅C are fixed 1.00 m apart, with the +12.0 Β΅C charge to the right of the +3.00 Β΅C. The resultant force produced on a βˆ’2.00 nC charge by the fixed charges can be described by taking positive horizontal force magnitude as being to the right and positive vertical force magnitude as being upward.

Find the net force halfway between the two fixed charges.

  • A 4 . 3 0 Γ— 1 0  οŠͺ N
  • B 5 . 1 1 Γ— 1 0  οŠͺ N
  • C 2 . 3 5 Γ— 1 0  οŠͺ N
  • D 7 . 4 2 Γ— 1 0  οŠͺ N
  • E 6 . 4 7 Γ— 1 0  οŠͺ N

Find the net force 0.500 m to the left of the +3.00 Β΅C charge.

  • A 2 . 3 5 Γ— 1 0  οŠͺ N
  • B 7 . 4 2 Γ— 1 0  οŠͺ N
  • C 5 . 1 1 Γ— 1 0  οŠͺ N
  • D 3 . 1 2 Γ— 1 0  οŠͺ N
  • E 4 . 3 0 Γ— 1 0  οŠͺ N

Find the net force 0.500 m above the +12.0 Β΅C charge in a direction perpendicular to the line joining the two fixed charges.

  • A ο€Ή βˆ’ 2 . 7 6 Γ— 1 0 βˆ’ 8 . 7 7 Γ— 1 0     οŠͺ i j N
  • B ο€Ή βˆ’ 3 . 2 0 Γ— 1 0 βˆ’ 8 . 0 6 Γ— 1 0     οŠͺ i j N
  • C ο€Ή βˆ’ 2 . 6 0 Γ— 1 0 βˆ’ 9 . 3 6 Γ— 1 0     οŠͺ i j N
  • D ο€Ή βˆ’ 1 . 9 5 Γ— 1 0 βˆ’ 6 . 2 9 Γ— 1 0     οŠͺ i j N
  • E ο€Ή βˆ’ 2 . 0 8 Γ— 1 0 βˆ’ 7 . 0 6 Γ— 1 0     οŠͺ i j N

Q4:

What is the net force on the 5.0-Β΅C charge shown?

  • A ( βˆ’ 0 . 0 9 0 βˆ’ 0 . 0 6 0 ) i j N
  • B ( βˆ’ 0 . 0 2 0 βˆ’ 0 . 0 3 0 ) i j N
  • C ( βˆ’ 0 . 0 3 0 βˆ’ 0 . 0 6 0 ) i j N
  • D ( βˆ’ 0 . 0 6 0 βˆ’ 0 . 0 1 0 ) i j N
  • E ( βˆ’ 0 . 0 6 0 βˆ’ 0 . 0 3 0 ) i j N

Q5:

A charge π‘ž=+2.0Β΅C is placed at the point 𝑃 shown. What is the force exerted on π‘ž? Assume that force directed toward the right corresponds to positive values.

Q6:

Point charges 𝑄=65 Β΅C and 𝑄=35 Β΅C are placed so that π‘„οŠ¨ is 2.0 m left of π‘„οŠ§. A charge π‘„οŠ© is placed between π‘„οŠ§ and π‘„οŠ¨. At what distance to the right of π‘„οŠ¨ must π‘„οŠ© be placed so that the net force on it is zero?

Q7:

Point charges 𝑄=3.0¡C and 𝑄=6.0¡C have the position vectors rijk=(3.00βˆ’1.00+6.00)m and rijk=(7.00+6.00βˆ’3.00)m respectively. What magnitude force is exerted by π‘„οŠ¨ on π‘„οŠ§?

  • A 9 6 Γ— 1 0   N
  • B 2 3 Γ— 1 0   N
  • C 1 1 Γ— 1 0  οŠͺ N
  • D 1 . 2 Γ— 1 0   N
  • E 2 . 3 Γ— 1 0   N

Q8:

What is the magnitude of the net electric force on the charge located at the upper corner of the triangle shown? The triangle’s sides have a length of 1.0 m and the value of π‘ž is 5.0 Β΅C.

Q9:

The charges 𝑄=5.0Γ—10C, 𝑄=βˆ’4.0Γ—10C, and 𝑄=βˆ’3.0Γ—10C are placed at the corners of the triangle shown. What is the magnitude of the net force on π‘„οŠ§?

  • A 3 . 2 Γ— 1 0   N
  • B 1 2 Γ— 1 0   N
  • C 1 . 2 Γ— 1 0   N
  • D 2 . 0 Γ— 1 0  οŠͺ N
  • E 2 . 3 Γ— 1 0  οŠͺ N

Q10:

Point charges 𝑄=0.0050nC and 𝑄=0.020nC are fixed at rij=(9.00+3.50)m and rij=(6.50βˆ’2.00)m respectively. What is the magnitude of the electric force on π‘„οŠ¨ due to π‘„οŠ§?

  • A 0 . 6 7 Γ— 1 0   οŠͺ N
  • B 4 . 5 Γ— 1 0   οŠͺ N
  • C 3 . 2 Γ— 1 0   οŠͺ N
  • D 2 . 5 Γ— 1 0   οŠͺ N
  • E 3 6 Γ— 1 0   οŠͺ N

Q11:

The circular arc shown carries a charge per unit length πœ†=0.0010πœƒcos, where πœƒ is measured from the π‘₯-axis, π‘Ÿ=70.0 cm, and πœƒ=30∘. What is the magnitude of the electric field at the origin?

  • A 3 6 Γ— 1 0  N/C
  • B 1 . 1 Γ— 1 0  N/C
  • C 1 4 Γ— 1 0  N/C
  • D 1 1 Γ— 1 0  N/C
  • E 0 . 2 5 Γ— 1 0  N/C

Q12:

Three charges are placed at the corners of a parallelogram as shown in the diagram. The parallelogram’s horizontal sides are 2.00 m in length, its diagonal sides are 1.00 m in height and angled at 30.0∘, and the charges are exact multiples of 𝑄=6.0Β΅C. The point 𝑃 corresponds to the unoccupied upper right-hand corner of the parallelogram.

What is the magnitude of the electric field at 𝑃?

  • A 1 0 Γ— 1 0  N/C
  • B 9 . 8 Γ— 1 0  N/C
  • C 1 1 0 Γ— 1 0  N/C
  • D 3 . 2 Γ— 1 0  N/C
  • E 1 2 Γ— 1 0  N/C

If a test charge of 4.0 Β΅C is placed at 𝑃, what is the magnitude of the force on the charge?

Q13:

Three charges are placed at three of the corners of a square, as shown in the diagram. The square’s side length π‘Ž=0.500m and the charges are exact multiples of π‘ž=8.0Β΅C. The point 𝑃 corresponds to the unoccupied lower right-hand corner of the square.

What is the electric field vector at the point 𝑃?

  • A ( βˆ’ 8 . 9 + 8 . 9 ) Γ— 1 0 i j  N/C
  • B ( βˆ’ 3 2 + 2 3 ) Γ— 1 0 i j  N/C
  • C ( βˆ’ 1 1 + 1 1 ) Γ— 1 0 i j  N/C
  • D ( βˆ’ 1 3 + 1 3 ) Γ— 1 0 i j  N/C
  • E ( βˆ’ 1 0 + 1 0 ) Γ— 1 0 i j  N/C

If a test charge of 2.0 Β΅C is placed at the point 𝑃, what is the force vector at 𝑃?

  • A ( βˆ’ 9 . 2 + 3 . 2 ) i j N
  • B ( βˆ’ 2 . 3 + 6 . 2 ) i j N
  • C ( βˆ’ 3 2 + 1 4 ) i j N
  • D ( βˆ’ 2 . 3 + 2 . 3 ) i j N
  • E ( 2 . 6 βˆ’ 2 . 6 ) i j N

Q14:

What is the force on the 2.0 Β΅C charge placed at the center of the square shown?

  • A ( βˆ’ 0 . 0 2 5 βˆ’ 0 . 0 2 5 ) Γ— 1 0 i j  N
  • B ( 0 . 0 2 5 + 0 . 0 2 5 ) Γ— 1 0 i j  N
  • C ( βˆ’ 0 . 0 3 2 βˆ’ 0 . 0 3 2 ) Γ— 1 0 i j  N
  • D ( βˆ’ 0 . 0 6 5 βˆ’ 0 . 0 6 7 ) Γ— 1 0 i j  N
  • E ( βˆ’ 0 . 0 3 6 βˆ’ 0 . 0 7 4 ) Γ— 1 0 i j  N

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