Find the magnitude of the magnetic flux through the floor of a house that measures 21m by 13m . Assume that the Earth's magnetic field at the location of the house has a horizontal component of 2.4×10−5 T pointing north, and a downward vertical component of 4.3×10−5 T .
I can't seem to get the correct answer so i think I might be going about the problem the wrong way.
This is what I did.
Bx= 2.4x10-5 T
By= 4.3x10-5 T
Bnet= (Bx^2 + By^2)^.5 = 4.9x10-5 T
angle= tan^-1(By/Bx)= 60.83
A= 21m x 13m= 273m^2
Magnetic flux= Bcos angle A
magnetic flux= .00651 Wb
My answer was incorrect, any ideas what the right way to approach this problem is??
To find the magnitude of the magnetic flux through the floor of the house, you need to use the formula:
Magnetic flux = B * A * cos(angle)
where B is the magnetic field, A is the area, and angle is the angle between the magnetic field and the normal to the surface.
In this case, the magnetic field has both a horizontal component (Bx) and a downward vertical component (By). To find the total magnetic field (B), you can use Pythagoras' theorem:
B = sqrt(Bx^2 + By^2) = sqrt((2.4x10^-5 T)^2 + (4.3x10^-5 T)^2) = 4.95x10^-5 T
Next, to find the angle, you can use the inverse tangent function (tan^-1):
angle = tan^-1(By/Bx) = tan^-1((4.3x10^-5 T)/(2.4x10^-5 T)) = 63.43 degrees
Finally, you can substitute the values in the formula to find the magnetic flux:
Magnetic flux = (4.95x10^-5 T) * (21 m * 13 m) * cos(63.43 degrees)
Calculating this, you should obtain the correct magnitude of the magnetic flux through the floor of the house.
To calculate the magnitude of the magnetic flux through the floor of the house, you need to consider the area vector perpendicular to the floor. Here's how you can solve it:
1. Calculate the magnitude of the area vector. The area vector is perpendicular to the floor surface, which means it points vertically upward. Since the floor is horizontal, the area vector magnitude is equal to the floor area: A = (21 m) × (13 m) = 273 m².
2. Calculate the magnitude of the magnetic field vector. The Earth's magnetic field has both horizontal (Bx) and vertical (By) components given. The magnitude of the magnetic field vector B is given by B = sqrt(Bx² + By²) = sqrt((2.4 × 10^(-5) T)² + (4.3 × 10^(-5) T)²) = 4.92 × 10^(-5) T.
3. Calculate the angle between the area vector and the magnetic field vector. Since the area vector is perpendicular to the floor, it is also perpendicular to the magnetic field vector. Therefore, the angle between them is 90 degrees.
4. Calculate the magnetic flux through the floor. The magnetic flux Φ is given by Φ = B * A * cosθ, where θ is the angle between the magnetic field vector and the area vector. Since θ = 90 degrees, cosθ = cos(90°) = 0. Therefore, the magnetic flux through the floor is:
Φ = (4.92 × 10^(-5) T) * 273 m² * 0
Φ = 0 Wb
So, the correct answer is that the magnetic flux through the floor of the house is 0 Weber (Wb).