A circular area with a radius of 7.40 lies in the x-y plane. 1.What is the magni

Question

A circular area with a radius of 7.40 lies in the x-y plane. 1.What is the magnitude of the magnetic flux through this circle due to a uniform magnetic field B= 0.232 T that points in the +z direction? 2.What is the magnitude of the magnetic flux through this circle due to a uniform magnetic field B= 0.232 T that points at an angle of 52.5 degrees from the direction? 3.What is the magnitude of the magnetic flux through this circle due to a uniform magnetic field B= 0.232 T that points in the +y direction?

Explanation / Answer

The quantity symbolised by B and measured in units of T (Teslas) is magnetic flux density. Magnetic field is a completely different quantity. It is symbolised as H and is measured in units of A/m (Amps per metre). B & H are related thus : H = B/u where u is the permeability of the medium in which the quantities are measured. Your question does not say anything about u, so the field corresponding to a flux density of 0.249T cannot be calculated. If the medium is air or vacuum, the permeability of free space u0 could be used. I will answer the question as though all references to magnetic field are replaced by references to flux density. Talk to your teacher about the necessity of using the correct names and units for physical quantities. A) you do not say what the units of the radius are. I will assume that they are m; this gives an area of 172m^2. When a uniform flux density passes through a plane surface of area A, the normal to which makes an angle (a) relative to the direction of the B vector, the flux passing through A is F = B*A*cos(a) In this case a = 0deg, so F = 0.249*172 = 42.8Wb B) In this example, F = 42.8*cos(53.6) = 25.4Wb C) a = 90deg, F = 0Wb

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