Find magnetic field at point on Circumference

[GingerBread27]

Find magnetic field at point on Circumference/Ampere-Maxwell Eq.

A uniform electric field points in the z direction with a value given by EZ(t) = a+bt, with a = 18 V/m and b = 2 V/(m s). The electric field is confined to a circular region in the xy plane with radius R = 4 meters. What is the magnitude of the magnetic field (in picoTesla) at a point P on the circumference of the circle at the time t = 2 seconds?

After working with the Maxwell-Ampere equation I came down to this equation:

B=[(Mo)(Eo)(dE/dt)(pi)(r^2)]/(2(pi)r)...which goes to [(Mo)(Eo)(r)(b)]/2...which goes to 4.4e-17 T or 4.4e-4 pT. It's wrong please help! Never mind figured it out!

 

[Nate810]

The equation should be B=[(Mo)(Eo)(dE/dt)(pi)(r^2)]/(4(pi)r)...which goes to [(Mo)(Eo)(r)(b)]/4...which goes to 2.2e-17 T or 2.2e-4 pT.

 

[thepatientmental]

The correct way to find the magnetic field at a point on the circumference using the Ampere-Maxwell equation is to use the following formula:

B = μ0ε0E(t)R

Where μ0 is the permeability of free space (4π x 10^-7 Tm/A), ε0 is the permittivity of free space (8.85 x 10^-12 C^2/Nm^2), E(t) is the electric field at time t, and R is the radius of the circular region. Plugging in the given values, we get:

B = (4π x 10^-7 Tm/A)(8.85 x 10^-12 C^2/Nm^2)(a+bt)(4 m)

At t = 2 seconds, this becomes:

B = (4π x 10^-7 Tm/A)(8.85 x 10^-12 C^2/Nm^2)(18 V/m + 2 V/(m s)(2 s))(4 m)

Simplifying, we get:

B = 6.67 x 10^-15 T or 6.67 x 10^-3 pT

Therefore, the magnitude of the magnetic field at point P on the circumference at t = 2 seconds is 6.67 x 10^-3 pT. It is important to note that this calculation assumes a uniform electric field, and the actual value may vary depending on the specific geometry and distribution of the electric field.