A Wire Inside a Solenoid

Q. A 3.0 cm wire carrying a current of 10 A is placed inside a solenoid perpendicular to its axis. The magnetic field inside the solenoid is given to be 0.27 T. What is the magnetic force on the wire, in newtons? expects 0.081 N

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The web of concepts

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Q. A 3.0 cm $l = 3.0$ cm wire carrying a current of 10 A $I = 10$ A is placed inside a solenoid perpendicular to its axis. The magnetic field inside the solenoid is given to be 0.27 T $B = 0.27$ T. What is the magnetic force on the wire, in newtons?

The playground

Inputs

length

l

3 cm

current

I

10 A

field

B

0.27 T

Outputs

force

F

The solution

Solved with MagneticForce

Given

$l = 3.0$ cm
$I = 10$ A
$B = 0.27$ T

Find $F$ .

Working

$l = 3.0$ cm $= 0.03$ m
force on a wire across a field(wire) $F = I \cdot l \cdot B$
$F = 10 \cdot 0.03 \cdot 0.27$
$F = 0.081$ N
$F \approx 0.081$ Nto 2 significant figures

Conclusion

The field inside a solenoid runs along its axis, so a wire across the axis stands square across the field and feels the full force.

The Ruby

1require_relative "../physics"23question :a_wire_inside_a_solenoid do4  kind :numerical5  describes "A %{length} wire carrying a current of %{current} is placed inside a solenoid perpendicular to its " \6            "axis. The magnetic field inside the solenoid is given to be %{field}. %{force}, in newtons?"7  given length: "3.0 cm"8  given current: "10 A"9  given field: "0.27 T"10  asks force: "What is the magnetic force on the wire"11end

1require_relative "../questions/a_wire_inside_a_solenoid"2require_relative "../science/moving_charges_and_magnetism/magnetic_force"34solve :a_wire_inside_a_solenoid, using: MagneticForce do5  objects :wire67  take length: wire.length_in_the_field8  take current: wire.current9  take field: B1011  force = wire.force_on_a_wire12  answer force:, in: "N", figures: 21314  conclusion "The field inside a solenoid runs along its axis, so a wire across the axis stands square across " \15             "the field and feels the full force."16end

1require_relative "../solutions/a_wire_inside_a_solenoid"23play_with :a_wire_inside_a_solenoid do4  title "A Wire Inside a Solenoid"5end

The laws

quantity	written	units	within	from
pi	$π$	—	0 … ∞	MagneticForce
elementary charge	$e$	C	—	MagneticForce
gravity	$g$	m/s²	—	MagneticForce
magnetic field	$B$	T	—	MagneticForce
mass	$m$	kg	0 … ∞	MagneticForce
charge	$q$	C	—	MagneticForce
speed	$v$	m/s	—	MagneticForce
current	$I$	A	—	MagneticForce
length in the field	$l$	m	—	MagneticForce
force on a wire	$F$	N	—	MagneticForce
force per length	$f$	N/m	—	MagneticForce
radius of the path	$r$	m	—	MagneticForce
angle to the field	$θ$	—	0 … 3.142	MagneticForce
frequency of revolution	$ν$	Hz	—	MagneticForce
force on a wire on ground	$F_{g}$	N	—
current of ground	$I_{g}$	A	—
length in the field of ground	$l_{g}$	m	—
force on a wire on wire	$F$	N	—
current of wire	$I$	A	—
length in the field of wire	$l$	m	—
force per length on ground	$f_{g}$	N/m	—
angle to the field of ground	$θ_{g}$	—	0 … 3.142
force per length on wire	$f$	N/m	—
angle to the field of wire	$θ$	—	0 … 3.142
radius of the path of ground	$r_{g}$	m	—
mass of ground	$m_{g}$	kg	0 … ∞
speed of ground	$v_{g}$	m/s	—
charge of ground	$q_{g}$	C	—
radius of the path of wire	$r$	m	—
mass of wire	$m$	kg	0 … ∞
speed of wire	$v$	m/s	—
charge of wire	$q$	C	—
frequency of revolution of ground	$ν_{g}$	Hz	—
frequency of revolution of wire	$ν$	Hz	—

F_{w} = I_{w} \cdot l_{w} \cdot B

force on a wire across a field

f_{w} = I_{w} \cdot B \cdot \sin θ_{w}

force on each metre of wire

r_{c} = \frac{m_{c} \cdot v_{c}}{q_{c} \cdot B}

a charge circles in a field

v_{c} = 2 \cdot π \cdot r_{c} \cdot ν_{c}

once round the circle

F_{g} = I_{g} \cdot l_{g} \cdot B

force on a wire across a field(ground)

F = I \cdot l \cdot B

force on a wire across a field(wire)

f_{g} = I_{g} \cdot B \cdot \sin θ_{g}

force on each metre of wire(ground)

f = I \cdot B \cdot \sin θ

force on each metre of wire(wire)

r_{g} = \frac{m_{g} \cdot v_{g}}{q_{g} \cdot B}

a charge circles in a field(ground)

r = \frac{m \cdot v}{q \cdot B}

a charge circles in a field(wire)

v_{g} = 2 \cdot π \cdot r_{g} \cdot ν_{g}

once round the circle(ground)

v = 2 \cdot π \cdot r \cdot ν

once round the circle(wire)