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 ๐‘ž = + 5 0 1 ยต C and ๐‘ž = โˆ’ 2 5 2 ยต C are placed 1.0 m apart. What is the magnitude of the force on a third charge ๐‘ž = + 2 0 3 ยต C placed midway between and ๐‘ž 1 and ๐‘ž 2 ?

Q2:

Two fixed particles, each of charge + 5 . 0 ร— 1 0 โˆ’ 6 C, are 24 cm apart. What magnitude force do they exert on a third particle of charge โˆ’ 2 . 5 ร— 1 0 โˆ’ 6 C that is 13 cm from each of them?

Q3:

Two charges + 3 . 0 0 ยตC and + 1 2 . 0 ยตC are fixed 1.00 m apart, with the + 1 2 . 0 ยตC charge to the right of the + 3 . 0 0 ยตC. The resultant force produced on a โˆ’ 2 . 0 0 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 ร— 1 0 ๏Šฑ ๏Šช N
  • B 2 . 3 5 ร— 1 0 ๏Šฑ ๏Šช N
  • C 5 . 1 1 ร— 1 0 ๏Šฑ ๏Šช N
  • D 6 . 4 7 ร— 1 0 ๏Šฑ ๏Šช N
  • E 7 . 4 2 ร— 1 0 ๏Šฑ ๏Šช N

Find the net force 0.500 m to the left of the + 3 . 0 0 ยตC charge.

  • A 3 . 1 2 ร— 1 0 ๏Šฑ ๏Šช N
  • B 5 . 1 1 ร— 1 0 ๏Šฑ ๏Šช N
  • C 4 . 3 0 ร— 1 0 ๏Šฑ ๏Šช N
  • D 2 . 3 5 ร— 1 0 ๏Šฑ ๏Šช N
  • E 7 . 4 2 ร— 1 0 ๏Šฑ ๏Šช N

Find the net force 0.500 m above the + 1 2 . 0 ยตC charge in a direction perpendicular to the line joining the two fixed charges.

  • A ๏€บ โˆ’ 1 . 9 5 ร— 1 0 โƒ‘ ๐‘– โˆ’ 6 . 2 9 ร— 1 0 โƒ‘ ๐‘— ๏† ๏Šฑ ๏Šซ ๏Šฑ ๏Šช N
  • B ๏€บ โˆ’ 2 . 0 8 ร— 1 0 โƒ‘ ๐‘– โˆ’ 7 . 0 6 ร— 1 0 โƒ‘ ๐‘— ๏† ๏Šฑ ๏Šซ ๏Šฑ ๏Šช N
  • C ๏€บ โˆ’ 2 . 7 6 ร— 1 0 โƒ‘ ๐‘– โˆ’ 8 . 7 7 ร— 1 0 โƒ‘ ๐‘— ๏† ๏Šฑ ๏Šซ ๏Šฑ ๏Šช N
  • D ๏€บ โˆ’ 2 . 6 0 ร— 1 0 โƒ‘ ๐‘– โˆ’ 9 . 3 6 ร— 1 0 โƒ‘ ๐‘— ๏† ๏Šฑ ๏Šซ ๏Šฑ ๏Šช N
  • E ๏€บ โˆ’ 3 . 2 0 ร— 1 0 โƒ‘ ๐‘– โˆ’ 8 . 0 6 ร— 1 0 โƒ‘ ๐‘— ๏† ๏Šฑ ๏Šซ ๏Šฑ ๏Šช N

Q4:

What is the net force on the 5.0-ยตC charge shown?