A Dipole on the z Axis

Q. A system has two charges qA = 2.5 × 10⁻⁷ C and qB = –2.5 × 10⁻⁷ C located at points A: (0, 0, –15 cm) and B: (0, 0, +15 cm), respectively. What is the electric dipole moment of the system, in C m? expects 7.5 × 10⁻⁸ C m

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The web of concepts

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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?

The playground

Inputs

charge

q

2.5e-07 C

Outputs

moment

p

The solution

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 Ruby

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

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

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

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)