The figure below shows a uniform magnetic field B confined to a cylindrical volu

Question

The figure below shows a uniform magnetic field B confined to a cylindrical volume of radius R. The magnitude of B is decreasing at a constant rate of 14.8 mT what are (a) the x-component, (b) the y-component, and (c) the z-component of the initial acceleration of an electron released at point a (radial distance r = 4.80 cm)? What are (d) the x-component, (e) the y-component, and (f) the z-component of the initial acceleration of an electron released at point b (r 0 cm)? what are (g) the x-component, (h) the y-component, and (i) the z-component of the initial acceleration of an electron released at point c (radial distance r = 4.80 cm)? (a) Number (b) Number (c) Number (d) Number (e) Number (f) Number (g) Number (h) Number (i) Number Units Units Units Units Units Units Units Units Units

Explanation / Answer

If you imagine a circular path around the origin with a radius equal to 0.048 m,

the area is equal to PI * 0.048 * 0.048 = 0.0072 sq. m.

Rate of change of flux = 0.0148 * 0.0072 per sec = electric field

Therefore electric field = 0.000107 volt/m

Force on the electron can be found by multiplying the electronic charge -e = -1.60217646 × 10-19 coulombs with the electric field. (F=Eq)

the direction of electric field (and hence the force) is given by Faraday's law.

Acceleration can be found by F=ma.

Here due to symmetric B field distribution. the electric field vector is such that electric lines of force are concentric around axis of the cylinder.

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