Concept:Magnetic flux depends on the angle \( \theta \) between the magnetic field vector and the normal vector to the area.
Formula:$$ \Phi = BA \cos(\theta) $$
Solution:- Identify the givens: Magnitude of flux \( |\Phi| = 10 \ \text{Wb} \), \( B = 1 \ \text{T} \), \( A = 10 \ \text{m}^2 \).
- Substitute into the formula: \( 10 = (1)(10) \cos(\theta) \).
- Solve for the cosine term: \( \cos(\theta) = 1 \) (or \( -1 \) if we consider the absolute magnitude of the flux).
- Angles that satisfy \( |\cos(\theta)| = 1 \) are \( 0^\circ \) and \( 180^\circ \).
- Since \( 0^\circ \) is not in the options, the correct answer must be \( 180^\circ \), which gives a flux of \( -10 \ \text{Wb} \) (magnitude is \( 10 \)).
Why other options are incorrect:Option B (\( 360^\circ \)) is a full rotation yielding the same as \( 0^\circ \), but conventionally \( 180^\circ \) is used for anti-parallel vectors. Option C yields zero flux. Option D yields \( 7.07 \ \text{Wb} \).
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