Question

In each of five situations, two point charges (Q1, Q2) are separated by a distance d. Rank them in order of the magnitude of the electric force on Q1, from largest to smallest.

Answer 1

Concept:

The magnitude of the electric force between the two charges is

F = k|Q1||Q2|/r2

 

Here |Q1| and |Q2| are the magnitudes of the charges, k is the proportional constant, and r is the distance between the charges.

 

Solution:

(a)

Conversion of the charge from micro coulombs to coulombs:

Magnitude of the first charge is

|Q1| = 1 µC

           = (1 µC)(10-6 C/1 µC)

           = 1 × 10-6 C

 

Magnitude of the second charge is

|Q2| = 2 µC

           = (2 µC)(10-6 C/1 µC)

           = 2 × 10-6 C

 

The magnitude of the force between the charges is

F = k|Q1||Q2|/d2

 

Substitute 1 × 10-6 C for the magnitude of the first charge, 2 × 10-6 for the magnitude of the second charge, 1 m for the distance between the charges, 8.99 × 109 N ∙m2/C2 for the proportional constant.

 

F = (8.99 × 109 N∙m2/C2)(1 × 10-6 C)(2 × 10-6 C)/(1 m)2

   = (17.98 × 10-3 N)(1 mN/10-3 N)

   = 17.98 mN

 

(b)

Conversion of the charge from micro coulombs to coulombs:

Magnitude of the first charge is

|Q1| = 2 µC

           = (2 µC)(10-6 C/1 µC)

           = 2 × 10-6 C

 

Magnitude of the second charge is

|Q2| = 1 µC

          = (1 µC)(10-6 C/1 µC)

          = 1 × 10-6 C

 

The magnitude of the force between the charges is

F = k|Q1||Q2|/d2

 

Substitute 2 × 10-6 C for the magnitude of the first charge, 1 × 10-6 C for the magnitude of the second charge, 1 m for the distance between the charges, 8.99 × 109 N∙m2/C2 for the proportional constant.

 

F = (8.99 × 109 N∙m2/C2)(1 × 10-6 C)(2 × 10-6 C)/(1 m)2

   = (17.98 × 10-3 N)(1 mN/10-3 N)

   = 17.98 mN

 

(c)

Conversion of the charge from micro coulombs to coulombs:

Magnitude of the first charge is

|Q1| = 2 µC

          = (2 µC)(10-6 C/1 µC)

          = 2 × 10-6 C

 

Magnitude of the second charge is

|Q2| = 4 µC

          = (4 µC)(10-6 C/1 µC)

          = 4 × 10-6 C

 

The magnitude of the force between the charges is

F = k|Q1||Q2|/d2

 

Substitute 2 × 10-6 C for the magnitude of the first charge, 4 × 10-6 C for the magnitude of the second charge, 4 m for the distance between the charges, 8.99 × 109 N∙m2/C2 for the proportional constant.

F = (8.99 × 109 N∙m2/C2)(2 × 10-6 C)(4 × 10-6 C)/(4 m)2

   = (4.495 × 10-3 N)(1 mN/10-3 N)

   = 4.495 mN

 

(d)

Conversion of the charge from micro coulombs to coulombs:

Magnitude of the first charge is

|Q1| = 2 µC

          = (2 µC)(10-6 C/1 µC)

          = 2 × 10-6 C

 

Magnitude of the second charge is

|Q2| = 2 µC

          = (2 µC)(10-6 C/1 µC)

          = 2 × 10-6 C

 

The magnitude of the force between the charges is

F = k|Q1||Q2|/d2

 

Substitute 2 × 10-6 C for the magnitude of the first charge, 2 × 10-6 C for the magnitude of the second charge, 2 m for the distance between the charges, 8.99 × 109 N∙m2/C2 for the proportional constant.

 

F = (8.99 × 109 N∙m2/C2)(2 × 10-6 C)(2 × 10-6 C)/(2 m)2

   = (8.99 × 10-3 N)(1 mN/10-3 N)

   = 8.99 mN

 

(e)

Conversion of the charge from micro coulombs to coulombs:

Magnitude of the first charge is

|Q1| = 4 µC

          = (4 µC)(10-6 C/1 µC)

          = 4 × 10-6 C

 

Magnitude of the second charge is

|Q2| = 2 µC

          = (2 µC)(10-6 C/1 µC)

          = 2 × 10-6 C

 

The magnitude of the force between the charges is

F = k|Q1||Q2|/d2

 

Substitute 4 × 10-6 C for the magnitude of the first charge, 2 × 10-6 C for the magnitude of the second charge, 4 m for the distance between the charges, 8.99 × 109 N∙m2/C2 for the proportional constant.

 

F = (8.99 × 109 N∙m2/C2)(4 × 10-6 C)(2 × 10-6 C)/(4 m)2

   = (4.495 × 10-3 N)(1 mN/10-3 N)

   = 4.495 mN

 

The order of the forces from largest to smallest is (a) = (b) > (d) > (c) = (e).

The order of the forces from largest to smallest is (a) = (b) > (d) > (c) = (e).