# Some nagnetsm problems need to be solved as soon as possible!!! help!

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I have some problems that are hard for me, and they need to be solved in 1 day! Please somebody help me solve the following questions!!!

(a) Find the electric field corresponding to the electrostatic potential φ(x,y,z) = −αr,where r = |r| = (x² + y² + z²)^(1/2) and α is constant.

(b) The electrostatic field in some region of free space is E = b r, where b is constant.Find the charge density ρ(r) which generates this electric field.

(c) A magnetic field is described by B = 2xybi + y²aj, where i and j are unit vectors in the x-direction and y-direction respectively, and a and b are coordinate-independent constants. Use Maxwell’s equation for ▽·B to calculate the ratio a/b.

(d) A the magnetic field in a region is given by B = 4xyi − 2y²j + 3zk. Find the steady current density that produces the magnetic fielld.

(e) An air-filled parallel-plate capacitor has circular plates. The electric field in the air gap is everywhere perpendicular to the plates and is produced by a charge σ per unit area on the plates. This charge is increasing at a constant rate, resulting in a magnetic field B consisting of concentric circular field lines in the air gap. Find an expression for the magnitude B = |B| of B as a function of radial distance r from the axis of
the capacitor.
You may assume that the magnitude of the electric field everywhere between the
plates of the capacitor is given by E = σ/ε0.
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