A Dipole on the z Axis

solved DipoleInAField

Q. A system has two charges qA = 2.5 × 10⁻⁷ C $q = 2.5 \times 10^{−7}$ C and qB = –2.5 × 10⁻⁷ C $q = 2.5 \times 10^{−7}$ C located at points A: (0, 0, –15 cm) and B: (0, 0, +15 cm) $l = 30$ cm, respectively. What is the electric dipole moment of the system, in C m?

Inputs

charge

q

2.5e-07 C

Outputs

moment

p

How it's solved

Solved with DipoleInAField

Given

$q = 2.5 \times 10^{−7}$ C
$l = 30$ cm from “(0, 0, –15 cm) and B: (0, 0, +15 cm)”

Find $p$ .

Working

$l = 30$ cm $= 0.3$ m
moment of a pair of charges(dipole) $p = q \cdot l$
$p = 2.5 \times 10^{−7} \cdot 0.3$
$p = 7.5 \times 10^{−8}$ C m
$p \approx 7.5 \times 10^{−8}$ C mto 2 significant figures

Conclusion

Equal and opposite charges cancel in total, but held apart they make a dipole whose moment is the charge times the distance between them.

The web of concepts

given read from the words equation asked

The Ruby that solves it

The question and its solution are small Ruby files. The engine runs them.

question.rb

1require_relative "../physics"23question :a_dipole_on_the_z_axis do4  kind :numerical5  describes "A system has two charges qA = %{charge} and qB = –%{charge} located at points A: (0, 0, –15 cm) and " \6            "B: (0, 0, +15 cm), respectively. %{moment}, in C m?"7  given charge: "2.5e-7 C"8  asks moment: "What is the electric dipole moment of the system"9end

solution.rb

1require_relative "../questions/a_dipole_on_the_z_axis"2require_relative "../science/electrostatic_potential_and_capacitance/dipole_in_a_field"34solve :a_dipole_on_the_z_axis, using: DipoleInAField do5  objects :dipole67  take charge: dipole.charge89  deduce_from "(0, 0, –15 cm) and B: (0, 0, +15 cm)", dipole.length_of_the_dipole => "30 cm"1011  moment = dipole.dipole_moment12  answer moment:, in: "C m", figures: 21314  conclusion "Equal and opposite charges cancel in total, but held apart they make a dipole whose moment is the " \15             "charge times the distance between them."16end

playground.rb

1require_relative "../solutions/a_dipole_on_the_z_axis"23play_with :a_dipole_on_the_z_axis do4  title "A Dipole on the z Axis"5end

The laws it drew on

quantity	written	units	within	from
field strength	$E$	V/m	—	DipoleInAField
dipole moment	$p$	C m	—	DipoleInAField
angle to the field	$θ$	—	0 … 3.142	DipoleInAField
potential energy	$U$	J	—	DipoleInAField
heat given out	$Q$	J	—	DipoleInAField
charge	$q$	C	—	DipoleInAField
length of the dipole	$l$	m	—	DipoleInAField
torque	$τ$	J	—	DipoleInAField
dipole moment of ground	$p_{g}$	C m	—
charge of ground	$q_{g}$	C	—
length of the dipole of ground	$l_{g}$	m	—
dipole moment of dipole	$p$	C m	—
charge of dipole	$q$	C	—
length of the dipole of dipole	$l$	m	—
torque on ground	$τ_{g}$	J	—
angle to the field of ground	$θ_{g}$	—	0 … 3.142
torque on dipole	$τ$	J	—
angle to the field of dipole	$θ$	—	0 … 3.142

p_{d} = q_{d} \cdot l_{d}

moment of a pair of charges

τ_{d} (moment) = p_{d} \cdot E \cdot \sin θ_{d} (moment)

torque on a dipole

p_{g} = q_{g} \cdot l_{g}

moment of a pair of charges(ground)

p = q \cdot l

moment of a pair of charges(dipole)

τ_{g} = p_{g} \cdot E \cdot \sin θ_{g}

torque on a dipole(ground)

τ = p \cdot E \cdot \sin θ

torque on a dipole(dipole)