A spatially uniform magnetic field B changes with time and induces an electric f

Question

A spatially uniform magnetic field B changes with time and induces an electric field E in a region of three-dimensional space containing the origin. The electric field is E = k(−sin θ, cos θ) N/C at the point (x, y, z), where k = 5.3 and θ = arctan(y/x).

(a) What is the rate of change of the magnetic flux through the circle x 2 + y 2 = 4.0 m2 in the xy plane? Assume that the area normal points in the positive z direction.

(b) Assuming that the flux is zero at time t = 0 s, what is the flux through the circle when t = 10 s?

(c) What is the magnetic field strength at t = 10 s

Explanation / Answer

(a)the rate of change of magnetic flux is

(dO/dt) = B * (dA/dt) = B * 2 * ((dx/dt) + (dy/dt))

where B is magnetic field

(b)the flux through the circle at t = 10 s is

O = B * A

where A = 4.0 m^2

(c)we know that

v = (E/B)

or B = (E/v)

where B is magnetic field and v is the speed of electrons

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