Answer:
the value of the earth's magnetic field is 2.60×10^-3 T.
Explanation:
we know that:
ε = N×A×2×(ΔB/Δt)
ΔB = ε×Δt/2×N×A
Bf - Bi = ε×Δt/2×N×A
Bf -0 = (0.166)×(2.77×10^-3)/2×(500)×(π×(7.5×10^-3)^2)
Bf = 2.60×10^-3 T
Therefore, the value of the earth's magnetic field is 5.82×10^--5 T.
Answer:
The magnetic field would be B = 5.2 x [tex]10^{-5}[/tex] T
Explanation:
The voltage that is obtained when the magnetic flux of a coil is altered is the induced emf.
The induced emf E = rate of change of magnetic flux
When the loop axis is parallel to the Earth's magnetic field the initial flux
is;
φ1 = NBAcosθ
Final flux = 0
Therefore the change in flux is dφ = NBAcosθ - 0
dφ = NBAcosθ
Given
the induced emf E = 0.166 V
the time dt = 2.77 ms = 2.77 x [tex]10^{-3}[/tex] s
N = number of turns = 500
d = diameter = 15 cm /100 = 0.15 m
A = area of cross section = π[tex]d^{2}[/tex]/4 = π x (0.15m[tex])^{2}[/tex]/4 = 0.0176715 [tex]m^{2}[/tex]
B = magnetic field
The induced emf E can be expressed thus
E = dφ/dt
= NBAcosθ/dt
cosθ = 1
E =NBA/dt
0.166 = 500 x Bx 0.0176715/ 2.77 x [tex]10^{-3}[/tex]
0.166 x 2.77 x [tex]10^{-3}[/tex] = 500 x B x 0.0176715
0.00045982 = 8.83572934 B
B = 0.00045982 / 8.83572934
B = 0.00005204097
B = 5.2 x [tex]10^{-5}[/tex] T
Therefore the magnetic field would be B = 5.2 x [tex]10^{-5}[/tex] T
