A) if this energy is all in the form of a uniform electric field, what electric

Question

A) if this energy is all in the form of a uniform electric field, what electric field strength is present? B) if this energy is all in the form of a uniform magnetic field, what magnetic field strength is present? If the region is inside a solenoid & the current in the solenoid is 900A, what is the coil density (turns per unit length) sound the solenoid? Consider a cylindrical region of space 0.6m long & 0.3m in diameter. This region holds an energy of 4.24x10^4J. A) if this energy is all in the form of a uniform electric field, what electric field strength is present? B) if this energy is all in the form of a uniform magnetic field, what magnetic field strength is present? If the region is inside a solenoid & the current in the solenoid is 900A, what is the coil density (turns per unit length) sound the solenoid?

Explanation / Answer

The energy density of electric field is

U = ( 1/ 2) e_o E^2

energy / volume = ( 1/2) e_o E^2

E ^2 = 2 ( 4.24*10^4 J) / (pi)(1.5 m )^2 ( 0.6 m ) (8.85*10^ -12 )

E = 8.8959*10^ 7 N / C

b)

Magnitude of magnetic field is

B = E / c = ( 8.895*10^ 7 N /C) / ( 3 *10^ 8 m/s)

=0.298 T

c)

Magnetic field in side the solenoid

B = mu_o N i

N = B / mu_0 i

= (0.298 T) / ( 4*pi*10^ -7 )(900 A)

= 264.065 turns

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