A Coil Turned by a Field

Q. A 100 turn closely wound circular coil of radius 10 cm carries a current of 3.2 A. It is free to turn in a uniform magnetic field of 2 T, and has turned until its axis is at 90° to the field. What is the magnitude of the torque on the coil, in N m? expects 20 N m

What the draft establishes

Fills in once a draft is checked.

The web of concepts

given read from the words equation asked

The equations it used

None yet.

Check an answer

Q. A 100 $N = 100$ turn closely wound circular coil of radius 10 cm $R = 10$ cm carries a current of 3.2 A $I = 3.2$ A. It is free to turn in a uniform magnetic field of 2 T $B = 2$ T, and has turned until its axis is at 90° $θ = 90 °$ to the field. What is the magnitude of the torque on the coil, in N m?

The playground

Inputs

turns

N

100

radius

R

10 cm

current

I

3.2 A

field

B

2 T

angle

θ

90.00°

Outputs

torque

τ

The solution

Solved with CurrentLoopInAField

Given

$N = 100$
$R = 10$ cm
$I = 3.2$ A
$B = 2$ T
$θ = 90 °$

Find $τ$ .

Working

$R = 10$ cm $= 0.1$ m
moment of a round coil(coil) $m = N \cdot I \cdot π \cdot R^{2}$
$m = 100 \cdot 3.2 \cdot 3.14159265 \cdot {0.1}^{2}$
$m = 10.0530965$ m² A
torque on a coil(coil) $τ = m \cdot B \cdot \sin θ$
$τ = 10.0530965 \cdot 2 \cdot \sin 90 °$
$τ = 20.11$ N m
$τ = 20.106193$ J $= 20.106193$ N m
$τ \approx 20$ N mto 2 significant figures

Conclusion

The coil is a magnet of moment turns times current times area; the field twists it hardest when its axis stands across the field.

The Ruby

1require_relative "../physics"23question :a_coil_turned_by_a_field do4  kind :numerical5  describes "A %{turns} turn closely wound circular coil of radius %{radius} carries a current of %{current}. It is " \6            "free to turn in a uniform magnetic field of %{field}, and has turned until its axis is at %{angle} to " \7            "the field. %{torque}, in N m?"8  given turns: "100"9  given radius: "10 cm"10  given current: "3.2 A"11  given field: "2 T"12  given angle: "90 deg"13  asks torque: "What is the magnitude of the torque on the coil"14end

1require_relative "../questions/a_coil_turned_by_a_field"2require_relative "../science/moving_charges_and_magnetism/current_loop_in_a_field"34solve :a_coil_turned_by_a_field, using: CurrentLoopInAField do5  objects :coil67  take turns: coil.turns8  take radius: coil.radius9  take current: coil.current10  take field: B11  take angle: coil.angle_to_the_field1213  torque = coil.torque14  answer torque:, in: "N m", figures: 21516  conclusion "The coil is a magnet of moment turns times current times area; the field twists it hardest " \17             "when its axis stands across the field."18end

1require_relative "../solutions/a_coil_turned_by_a_field"23play_with :a_coil_turned_by_a_field do4  title "A Coil Turned by a Field"5end

The laws

quantity	written	units	within	from
pi	$π$	—	0 … ∞	CurrentLoopInAField
magnetic field	$B$	T	—	CurrentLoopInAField
current	$I$	A	—	CurrentLoopInAField
turns	$N$	—	—	CurrentLoopInAField
radius	$R$	m	0 … ∞	CurrentLoopInAField
area	$A$	m²	—	CurrentLoopInAField
magnetic moment	$m$	m² A	—	CurrentLoopInAField
angle to the field	$θ$	—	0 … 3.142	CurrentLoopInAField
torque	$τ$	J	—	CurrentLoopInAField
magnetic moment of ground	$m_{g}$	m² A	—
turns of ground	$N_{g}$	—	—
current of ground	$I_{g}$	A	—
radius of ground	$R_{g}$	m	0 … ∞
magnetic moment of coil	$m$	m² A	—
turns of coil	$N$	—	—
current of coil	$I$	A	—
radius of coil	$R$	m	0 … ∞
area of ground	$A_{g}$	m²	—
area of coil	$A$	m²	—
torque on ground	$τ_{g}$	J	—
angle to the field of ground	$θ_{g}$	—	0 … 3.142
torque on coil	$τ$	J	—
angle to the field of coil	$θ$	—	0 … 3.142

m_{c} = N_{c} \cdot I_{c} \cdot π \cdot {R_{c}}^{2}

moment of a round coil

m_{c} = N_{c} \cdot I_{c} \cdot A_{c}

moment of a flat coil

τ_{c} = m_{c} \cdot B \cdot \sin θ_{c}

torque on a coil

m_{g} = N_{g} \cdot I_{g} \cdot π \cdot {R_{g}}^{2}

moment of a round coil(ground)

m = N \cdot I \cdot π \cdot R^{2}

moment of a round coil(coil)

m_{g} = N_{g} \cdot I_{g} \cdot A_{g}

moment of a flat coil(ground)

m = N \cdot I \cdot A

moment of a flat coil(coil)

τ_{g} = m_{g} \cdot B \cdot \sin θ_{g}

torque on a coil(ground)

τ = m \cdot B \cdot \sin θ

torque on a coil(coil)