A magnetic field is oriented at an angle of 42 degrees to the normal of a rectangular area 5.5 cm by 6.8 cm. If the magnetic flux through this surface has a magnitude of 4.8 x 10^-5 Tm^2, what is the strength of the magnetic field?
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To find the strength of the magnetic field, we can use the formula:
Flux = Magnetic field strength * Area * Cos(angle)
Here, Flux refers to the magnitude of the magnetic flux, which is given as 4.8 x 10^-5 Tm^2. The area is given as 5.5 cm by 6.8 cm, which is equal to 0.055 m by 0.068 m. The angle is given as 42 degrees.
Let's substitute the known values into the formula and solve for the magnetic field strength.
Flux = Magnetic field strength * Area * Cos(angle)
4.8 x 10^-5 Tm^2 = Magnetic field strength * (0.055 m * 0.068 m) * Cos(42°)
Now, let's calculate the area:
Area = 0.055 m * 0.068 m
Area = 0.003740 m^2
Substituting the area back into the equation:
4.8 x 10^-5 Tm^2 = Magnetic field strength * 0.003740 m^2 * Cos(42°)
To solve for Magnetic field strength, divide both sides of the equation by (0.003740 m^2 * Cos(42°)):
Magnetic field strength = (4.8 x 10^-5 Tm^2) / (0.003740 m^2 * Cos(42°))
Now, calculate the value using a scientific calculator:
Magnetic field strength ≈ 0.294 T
Therefore, the strength of the magnetic field is approximately 0.294 Tesla.