Respuesta :
Answer:
The magnetic field 0.01m from the wire is 0.2T.
Explanation:
The magnetic field [tex]B[/tex] at a distance [tex]R[/tex] due to a wire carrying current [tex]I[/tex] is
[tex]B = \dfrac{\mu_o I}{2\pi R}.[/tex]
Now, let us call [tex]B_1[/tex] the magnetic field at [tex]R_1[/tex] and [tex]B_2[/tex] the magnetic field at [tex]R_2[/tex]:
[tex]B_1 = \dfrac{\mu_o I}{2\pi R_1},[/tex]
[tex]B_2 = \dfrac{\mu_o I}{2\pi R_2}.[/tex]
Dividing [tex]B_1[/tex] by [tex]B_2[/tex] we get
[tex]\dfrac{B_1}{B_2} = \dfrac{\dfrac{\mu_o I}{2\pi R_1} }{\dfrac{\mu_o I}{2\pi R_2} }[/tex]
[tex]\dfrac{B_1}{B_2} = \dfrac{\mu_o I}{2\pi R_1}* \dfrac{2\pi R_2}{\mu_oI}.[/tex]
[tex]\dfrac{B_1}{B_2} = \dfrac{2\pi R_2}{2\pi R_1}[/tex]
[tex]\boxed{\dfrac{B_1}{B_2} = \dfrac{R_2}{R_1}}[/tex]
Now we put in the numbers
[tex]B_1 = 0.1T,\: \: R_1 = 0.02m[/tex] and [tex]R_2 = 0.01m[/tex] to get:
[tex]\dfrac{0.1T}{B_2} = \dfrac{0.01m}{0.02m}[/tex]
[tex]\dfrac{0.1T}{B_2} = 0.5[/tex]
solving for [tex]B_2[/tex] we get:
[tex]B_2 = \dfrac{0.1T}{0.5}[/tex]
[tex]\boxed{B_2 = 0.2T}[/tex]
which is the magnetic field at 0.01 meters from the wire.
The magnetic field 0.01m from the wire is 0.2T.
What is magnetic field?
The magnetic field is the region of space where a charged object experiences magnetic force when it is moving.
The magnetic field B₁ at a distance 0.02 m due to a wire carrying current is
B₁ = μ₀I/2πR₁...................(1)
The magnetic field B₁ at a distance 0.01 m due to a wire carrying current is
B₂ = μ₀I/2πR₂....................(2)
Dividing both the equations, we get
B₁/B₂ = R₂/R₁
Substitute the values into the the above expression, we get
B₂ = 0.1 Tx 0.02 m/0.01 m
B₂ = 0.2T
Thus, the magnitude of the magnetic field 0.01 m from the same wire is 0.2T.
Learn more about magnetic field.
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