In a certain region of space, the magnetic field is not uniform. The magnetic field B̅ has both a z-component and a component that points radially away from or toward the z-axis. The z-component is given by B_z(Z) = βz, where β is a positive constant. The radial component B_rdepends only on r, the radial distance from the z-axis.

(a) Use Gauss€™s law for magnetism, Eq. (27.8), to find the radial compo-nent as a function of r.

(b) Sketch the magnetic field lines.

Eq. (27.8)

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fiö-c = B• dA closed surface) (magnetic flux through any