The intensity of the magnetic field is
Explanation:
According to Faraday's Law, the magnitude of the induced electromotive force (emf) in the coil corresponds to the rate of flux change that links through the coil:
(1)
where
N = 505 represents the number of turns in the coil
is the variation in magnetic flux through the coil
indicates the time interval
Rotating the coil from perpendicular to parallel alignment with the Earth's magnetic field results in the final flux equaling zero, making the magnitude of flux change simply the initial flux:
where
B denotes the intensity of the magnetic field
A signifies the area of the coil
represents the angle between the normal to the coil and the field
The area of the coil can be expressed as
where
outlines its radius
By substituting all values into equation (1) and solving for B, we obtain:
For further reading on magnetic fields:
Answer:
Earth's magnetic field strength is measured at 4.825 x 10⁻⁵ T
Explanation:
Provided details;
Turns count; N = 505 turns
Diameter of the circular loop, d = 15.5 cm
Average emf, V = 0.166 V
Change over time, t = 2.77 ms
Initially, the circular loop's plane is perpendicular to the Earth's magnetic field,
Finally, after the coil is rotated 90.0°,
Therefore, the calculated value of Earth's magnetic field is 4.825 x 10⁻⁵ T
Response:
The new resistance is half of the original resistance.
Explanation:
Resistance in a wire is represented by:
= resistivity of the material
L and A are the physical dimensions
If a wire is exchanged for one where all linear dimensions are doubled, i.e. l' = 2l and r' = 2r
The updated resistance of the wire can be calculated as follows:
The new resistance equals half of the original resistance. Thus, this provides the solution needed.
Answer:
a) τ = i ^ (y - z
) + j ^ (z Fₓ - x
) + k ^ (x
- y Fₓ)
b) τ = (-0.189i ^ -5.6 j ^ + 33.978k ^) N m
c) α = (-7.8 10⁻⁴ i ^ - 2.3 10⁻² j ^ + 1.4 10⁻¹ k ^) rad / s²
Explanation:
a) The torque can be expressed as
τ = r x F
To tackle this equation, using the determinant approach is the most straightforward method
The resulting expression is
τ = i ^ (y - z
) + j ^ (z Fₓ - x
) + k ^ (x
- y Fₓ)
b) Now let's compute
τ = i ^ (0.075 1.4 -0.035 8.4) + j ^ (0.035 2.8 - 4.07 1.4) + k ^ (4.07 8.4 - 0.075 2.8)
τ = i ^ (- 0.189) + j ^ (-5.6) + k ^ (33,978)
τ = (-0.189i ^ -5.6 j ^ + 33.978k ^) N m
c) To find angular acceleration, we use
τ = I α
α = τ / I
The moment of inertia being a scalar means that only the magnitude of each component changes, orientation remains constant.
α = (-0.189i^ -5.6 j^ + 33.978k^) / 241
α = (-7.8 10⁻⁴ i ^ - 2.3 10⁻² j ^ + 1.4 10⁻¹ k ^) rad / s²
Answer:
As indicated in the attached document
Explanation:
The comprehensive steps, mathematical reasoning, and manipulations are presented in the attachment.
