a) Solenoid 1 has self-inductance L 1 = 4.62 mH and solenoid 2 has self-inductan

Question

a) Solenoid 1 has self-inductance L1 = 4.62 mH and solenoid 2 has self-inductance L2 = 7.22 mH.
HINT: Use Kirchhoff's laws, and derive an expression similar to those for combinations of capacitors and combinations of resistors.
i. If L1 and L2 are placed in series with a battery, far enough apart so there is no interaction between them: find the total self-inductance of the circuit. Ls = mH
ii. If L1 and L2 are placed in parallel with a battery, far enough apart so there is no interaction between them: find the total self-inductance of the circuit. Lp = mH

b) A long wire is used to create a solenoid by tightly wrapping a single layer of adjacent turns around a long cylinder of wood. Now the solenoid is unwound, and then the same wire is used to create a new solenoid by tightly wrapping the same wire around a cylinder of wood whose radius is 8.13 times larger than the first. Neglecting any end effects: by what factor has the self-inductance of the solenoid changed? (If the initial self-inductance is Lo, the new self-inductance is L = kLo. Find k.)
NOTE: The radius, number of turns and length of the solenoid all change!


c) A long 1480 turn solenoid of length l = 2.18 m has self-inductance Lo = 4.62 mH when wrapped tightly around a wooden cylinder. If the cylinder is removed and the wires are bent so the turns are all squares (instead of circles), what would the self-inductance of this coil be now?
L = mH

d) Suppose a 919 turn solenoid has a circular cross section of radius r1 = 6.37 cm, length 9.47 m and carries a current I1 = 82 A. Find:
i. the energy stored in the magnetic field: U = _____________ J
ii. the energy density in the region inside the solenoid: u = J/m3

e) You want to create an electric field between parallel plates with the same energy density as a magnetic field inside a solenoid. Find the ratio (without units) of the magnitude of the electric field to the magnitude of the magnetic field of the solenoid:
E/B =

Explanation / Answer

a)

i) L = L1 + L2 = 4.62 + 7.22 = 11.8 mH

ii) L = 1/(1/L1+1/L2) = 1/(1/4.62 + 1/7.22) = 2.82 mH

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