A 0.055-T magnetic field passes through a circular ring of radius 3.1 cm at an angle of 16^∘ to

step 1 Hi, in the given problem, the magnitude of magnetic field is given as 0 .055 Tesla. Radius of th

A 0.055-T magnetic field passes through a circular ring of...

A $0.055-\mathrm{T}$ magnetic field passes through a circular ring of radius $3.1 \mathrm{~cm}$ at an angle of $16^{\circ}$ to the normal. Find the magnitude of the magnetic flux through the ring.

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Key Concepts

Magnetic Flux

Magnetic flux measures the quantity of magnetic field passing through a given area. It is defined as the product of the magnetic field’s magnitude, the area it penetrates, and the cosine of the angle between the field and the normal to that area, represented mathematically as ? = B * A * cos(?).

Magnetic Field

A magnetic field is a vector field around a magnet or a moving charge, describing the magnetic influence on other nearby moving charges or magnetic dipoles. Its magnitude is measured in teslas (T) and it has both magnitude and direction.

Surface Area of a Circle

The surface area of a circle is computed using the formula A = ?r², where r is the radius. This calculation is essential when determining the area over which the magnetic field is applied in flux calculations.

Angular Dependence in Flux Calculations

The orientation of the magnetic field relative to the surface plays a critical role in the calculation of magnetic flux. The angle between the magnetic field direction and the normal to the surface determines the effective component of the field that contributes to the flux, using the cosine of the angle.

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