Question

A 1 cm diameter copper cable is carrying 20 A with the current uniformly distributed throughout the cable. Point P is inside the cable, half way between the center and the outside. (i.e. 2.5 mm from the center) What is the curl of the magnetic field, H, at point P? What is the divergence of the magnetic flux density, B, at point P? (Put two answers in the box below.)

Answer 1

a)
`\\abla` × H = 25.46 A/cm²

b) Divergence of the magnetic flux at point P = 0

Step-by-step explanation:

a) What is the curl of the magnetic field, H, at point P

The curl of H is the current density.

According to Ampere's law,
`\\abla` × H = J

Where J = Current density

J =
`(I)/(A)`

Area, A =
`\pi R^(2)`

diameter, d = 1 cm

Radius, R = d/2 =1/2 = 0.5 cm = 0.005 m

A =
`\pi 0.005^(2)`

A = 0.00007855 m²

J = 20/0.00007855

J = 254614.895 A/m²

J = 254614.895 * 10⁻⁴ A/cm²

J = 25.46 A/cm²

`\\abla` × H = 25.46 A/cm²

b) What is the divergence of the magnetic flux density, B, at point P

According to Gauss' s law, at any point in a magnetic field,
`\\abla`.B = 0

Therefore, Divergence of B at point P = 0