East of a Wire Running South

solved MagneticFieldOfCurrents

Q. A long straight wire in the horizontal plane carries a current of 50 A $I = 50$ A in north to south direction. What is the magnitude of B at a point 2.5 m $d = 2.5$ m east of the wire, in teslas?

Inputs

current

I

50 A

distance

d

2.50 m

Outputs

field

B_{w}

How it's solved

Solved with MagneticFieldOfCurrents

Given

$I = 50$ A
$d = 2.5$ m

Find $B_{w}$ .

Working

field near a long straight wire(wire) $B_{w} = \frac{μ_{0} \cdot I}{2 \cdot π \cdot d}$
$B_{w} = \frac{1.25663706 \times 10^{−6} \cdot 50}{2 \cdot 3.14159265 \cdot 2.5}$
$B_{w} = 4 \times 10^{−6}$ T
$B_{w} \approx 4 \times 10^{−6}$ Tto 1 significant figure

Conclusion

The field circles the wire; by the right-hand rule, with the current running south, it points upward on the east side.

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 :east_of_a_wire_running_south do4  kind :numerical5  describes "A long straight wire in the horizontal plane carries a current of %{current} in north to south " \6            "direction. %{field} at a point %{distance} east of the wire, in teslas?"7  given current: "50 A"8  given distance: "2.5 m"9  asks field: "What is the magnitude of B"10end

solution.rb

1require_relative "../questions/east_of_a_wire_running_south"2require_relative "../science/moving_charges_and_magnetism/magnetic_field_of_currents"34solve :east_of_a_wire_running_south, using: MagneticFieldOfCurrents do5  objects :wire67  take current: wire.current8  take distance: wire.distance_from_the_wire910  field = wire.field_near_a_wire11  answer field:, in: "T", figures: 11213  conclusion "The field circles the wire; by the right-hand rule, with the current running south, it points " \14             "upward on the east side."15end

playground.rb

1require_relative "../solutions/east_of_a_wire_running_south"23play_with :east_of_a_wire_running_south do4  title "East of a Wire Running South"5end

The laws it drew on

quantity	written	units	within	from
pi	$π$	—	0 … ∞	MagneticFieldOfCurrents
permeability of free space	$μ_{0}$	N/A²	—	MagneticFieldOfCurrents
current	$I$	A	—	MagneticFieldOfCurrents
turns	$N$	—	—	MagneticFieldOfCurrents
radius	$R$	m	—	MagneticFieldOfCurrents
length of the coil	$L$	m	—	MagneticFieldOfCurrents
turns per length	$n$	m⁻¹	—	MagneticFieldOfCurrents
field at the centre	$B_{c}$	T	—	MagneticFieldOfCurrents
field inside	$B_{s}$	T	—	MagneticFieldOfCurrents
distance from the wire	$d$	m	—	MagneticFieldOfCurrents
field near a wire	$B_{w}$	T	—	MagneticFieldOfCurrents
field at the centre of ground	$B_{c,g}$	T	—
turns of ground	$N_{g}$	—	—
current of ground	$I_{g}$	A	—
radius of ground	$R_{g}$	m	—
field at the centre of wire	$B_{c}$	T	—
turns of wire	$N$	—	—
current of wire	$I$	A	—
radius of wire	$R$	m	—
turns per length of ground	$n_{g}$	m⁻¹	—
length of the coil of ground	$L_{g}$	m	—
turns per length of wire	$n$	m⁻¹	—
length of the coil of wire	$L$	m	—
field near a wire of ground	$B_{w,g}$	T	—
distance from the wire of ground	$d_{g}$	m	—
field near a wire of wire	$B_{w}$	T	—
distance from the wire of wire	$d$	m	—
field inside of ground	$B_{s,g}$	T	—
field inside of wire	$B_{s}$	T	—

B_{c,c} = \frac{μ_{0} \cdot N_{c} \cdot I_{c}}{2 \cdot R_{c}}

field at the centre of a coil

n_{c} = \frac{N_{c}}{L_{c}}

turns on each metre

B_{w,w} = \frac{μ_{0} \cdot I_{w}}{2 \cdot π \cdot d_{w}}

field near a long straight wire

B_{s,c} = μ_{0} \cdot n_{c} \cdot I_{c}

field inside a long solenoid

B_{c,g} = \frac{μ_{0} \cdot N_{g} \cdot I_{g}}{2 \cdot R_{g}}

field at the centre of a coil(ground)

B_{c} = \frac{μ_{0} \cdot N \cdot I}{2 \cdot R}

field at the centre of a coil(wire)

n_{g} = \frac{N_{g}}{L_{g}}

turns on each metre(ground)

n = \frac{N}{L}

turns on each metre(wire)

B_{w,g} = \frac{μ_{0} \cdot I_{g}}{2 \cdot π \cdot d_{g}}

field near a long straight wire(ground)

B_{w} = \frac{μ_{0} \cdot I}{2 \cdot π \cdot d}

field near a long straight wire(wire)

B_{s,g} = μ_{0} \cdot n_{g} \cdot I_{g}

field inside a long solenoid(ground)

B_{s} = μ_{0} \cdot n \cdot I

field inside a long solenoid(wire)