# 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 and are placed 1.0 m apart. What is the magnitude of the force on a third charge placed midway between and and ?

Q2:

Two fixed particles, each of charge C, are 24 cm apart. What magnitude force do they exert on a third particle of charge C that is 13 cm from each of them?

Q3:

Two charges µC and µC are fixed 1.00 m apart, with the µC charge to the right of the µC. The resultant force produced on a 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 N
• B N
• C N
• D N
• E N

Find the net force 0.500 m to the left of the µC charge.

• A N
• B N
• C N
• D N
• E N

Find the net force 0.500 m above the µC charge in a direction perpendicular to the line joining the two fixed charges.

• A N
• B N
• C N
• D N
• E N

Q4:

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

• A N
• B N
• C N
• D N
• E N

Q5:

A charge is placed at the point shown. What is the force exerted on ? Assume that force directed toward the right corresponds to positive values.

Q6:

Point charges µC and µC are placed so that is 2.0 m left of . A charge is placed between and . At what distance to the right of must be placed so that the net force on it is zero?

Q7:

Point charges and have the position vectors and respectively. What magnitude force is exerted by on ?

• A N
• B N
• C N
• D N
• E 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 is 5.0 µC.

Q9:

The charges , , and are placed at the corners of the triangle shown. What is the magnitude of the net force on ?

• A N
• B N
• C N
• D N
• E N

Q10:

Point charges and are fixed at and respectively. What is the magnitude of the electric force on due to ?

• A N
• B N
• C N
• D N
• E N

Q11:

The circular arc shown carries a charge per unit length , where is measured from the -axis, cm, and . What is the magnitude of the electric field at the origin?

• A N/C
• B N/C
• C N/C
• D N/C
• E 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 , and the charges are exact multiples of . The point corresponds to the unoccupied upper right-hand corner of the parallelogram.

What is the magnitude of the electric field at ?

• A N/C
• B N/C
• C N/C
• D N/C
• E N/C

If a test charge of 4.0 µC is placed at , 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 and the charges are exact multiples of . The point corresponds to the unoccupied lower right-hand corner of the square.

What is the electric field vector at the point ?

• A N/C
• B N/C
• C N/C
• D N/C
• E N/C

If a test charge of 2.0 µC is placed at the point , what is the force vector at ?

• A N
• B N
• C N
• D N
• E N

Q14:

What is the force on the 2.0 µC charge placed at the center of the square shown?

• A N
• B N
• C N
• D N
• E N