Question

The flux through a circular coil with radius of 0.075 m is 0.013 Wb when placed perpendicular to a magnetic field. What is the strength of the magnetic field?

show ALL work so I can see how to do it

Answer 1

Hi there!

The equation for magnetic flux is given by:

`\Phi_B = \oint B \cdot dA = B\cdot A`

Φ = Magnetic Flux (Wb)

B = Magnetic Field Strength (T)
A = Area of surface (m²)

**This is a dot product, which can be represented with cosφ. Since it is given that the loop is perpendicular to the field, its AREA VECTOR is parallel to the field, and since cos(180) = 1, the flux is equivalent to BA.

Since there is only one loop in the coil (not stated otherwise), we can use the unmodified equation above. Rearrange to solve for 'B'.

Recall that the area of a circle is A = πr².

`B = (\Phi_B)/(A)\\\\B = (0.013)/(\pi (0.075^2)) = \boxed{0.736 T}`