Question

In each of six situations, a particle (mass m, charge q) is located at a point where the electric field has magnitude E. No other forces act on the particles. Rank them in order of the magnitude of the particle’s acceleration, from largest to smallest.

Answer 1

Concept:

Electric force experienced by a point charge q in an electric field of strength E is

F = qE

 

Newton’s second law of motion is provides the formula for the net force as

F = ma

 

Here m is the mass of the particle and a is acceleration.

 

Comparing above two equations of the force,

ma = qE

 

Rearrange the above equation for the magnitude of the acceleration

a = qE/m

 

Solution:

 

(a)

Convert the mass of the particle from pictograms to kilograms

m = 6pg

    = (6 pg)(10-12 g/1 pg)(10-3 kg/1 g)

   = 6 × 10-15 kg

 

Convert the charge from nanocoulombs to coulombs

q = 5 nC

   = (5 nC)(10-9 C/1 nC)

   = 5 × 10-9 C

 

Magnitude of the acceleration of the particle is

a = qE/m

 

Substitute 6 × 10-15 kg for the mass of the particle, 5 × 10-9 C for the charge of the particle, and 40 N/C for the magnitude of the electric field.

 

a = {(5 × 10-9 C)(40 N/C)}/(6 × 10-15 kg)

   = 33.3 × 106 m/s2

 

(b)

Convert the mass of the particle from pictograms to kilograms

 

m = 3 pg

     = (3 pg)(10-12 g/1 pg)(10-3 kg/1 g)

     = 3 × 10-9 C

 

Convert the charge from nanocoulombs to coulombs

q = 5 nC

   = (5 nC)(10-9 C/ 1 nC)

   = 5 × 10-9 C

 

Magnitude of the acceleration of the particle is

a = qE/m

 

Substitute 3 × 10-15 kg for the mass of the particle, 5 × 10-9 C for the charge of the particle, and 40 N/C for the magnitude of the electric field.

 

a = {(5 × 10-9 C)(40 N/C)}/(3 × 10-15 kg)

   = 66.7 × 106 m/s2

 

(c)

Convert the mass of the particle from pictograms to kilograms

m = 3 pg

     = (3 pg)(10-12 g/1 pg)(10-3 kg/1 g)

     = 3 × 10-15 kg

 

Convert the charge from nanocoulombs to coulombs

q = 10 nC

   = (10 nC)(10-9 C/1 nC)

   = 10 × 10-9 C

 

Magnitude of the acceleration of the particle is

a = qE/m

 

Substitute 3 × 10-15 kg for the mass of the particle, 10 × 10-9 C for the charge of the particle, and 80 N/C for the magnitude of the electric field.

 

a = {(10 × 10-9 C)(40 N/C)}/(3 × 10-15 kg)

   = 267 × 106 m/s2

 

(d)

Convert the mass of the particle from pictograms to kilograms

m = 6 pg

    = (6 pg)(10-12 g/1 pg)(10-3 kg/1 g)

    = 6 × 10-15 kg

 

Convert the charge from nanocoulombs to coulombs

q = 1 nC

   = (1 nC)(10-9 C/1 nC)

   = 1 × 10-9 C

 

Magnitude of the acceleration of the particle is

a = qE/m

 

Substitute 6 × 10-15 kg for the mass of the particle, 1 × 10-9 C for the charge of the particle, and 200 N/C for the magnitude of the electric field.

 

a = {(1 × 10-9 C)(200 N/C)}/(6 × 106 m/s2)

  = 33.3 × 106 m/s2

 

(e)

Convert the mass of the particle from pictograms to kilograms

m = 1 pg

    = (1 pg)(10-12 g/ 1 pg)(10-3 kg/1 g)

    = 1 × 10-15 kg

 

Convert the charge from nanocoulombs to coulombs

q = 3 nC

   = (3 nC)(10-9 C/1 nC)

   = 3 × 10-9 C

 

Magnitude of the acceleration of the particle is

a = qE/m

 

Substitute 3 × 10-15 kg for the mass of the particle, 10 × 10-9 C for the charge of the particle, and 300 N/C for the magnitude of the electric field.

 

a = {(3 × 10-9 C)(300 N/C)}/(1 × 10-15 kg)

   = 900 × 106 m/s2

 

(f)

Convert the mass of the particle from pictograms to kilograms

m = 3 pg

    = (3 pg)(10-12 g/ 1 pg)(10-3 kg/1 g)

   = 3 × 10-15 kg

 

Convert the charge from nanocoulombs to coulombs

q = 1 nC

    = (1 nC)(10-9 C/1 nC)

    = 1 × 10-9 C

 

Magnitude of the acceleration of the particle is

a = qE/m

 

Substitute 3 × 10-15 kg for the mass of the particle, 10 × 10-9 C for the charge of the particle, and 80 N/C for the magnitude of the electric field.

 

a = {(1 × 10-9 C)(100 N/C)}/(3 × 10-15 kg)

   = 33.3 × 106 m/s2

 

The order of rank of the magnitude of particle acceleration from largest to smallest would be, (e) > (c) > (b) > (a) = (d) = (f).

The order of rank of the magnitude of particle acceleration from largest to smallest would be, (e) > (c) > (b) > (a) = (d) = (f).