A solenoid of length 1 m has 100 turns and carries a current of 1 A. (*this sett

Question

A solenoid of length 1 m has 100 turns and carries a current of 1 A. (*this setting is close to the actual configuration in the lab.) Assume the magnetic permeability of space is mu_0 = 1.26 times 10^-6 Tm/A . (i) Calculate the magnitude of magnetic field inside the solenoid. (ii) Compare the calculated magnetic field to typical magnetic fields around us; such as, the magnetic fields around the earth ( almostorequalto 0.5 mu T), due to refrigerator magnets (almostorequalto 5 mT) and inside medical MRIs (almostorequalto 1 T).

Explanation / Answer

here,

length , l = 1 m

number of turns , n = 100 turns

current , I= 1 A

a)

the magnituden of magnetic feild inside the solenoid , B = u0 * n * I/L

B = 1.26 * 10^-6 * 100 * 1/1

B = 1.26 * 10^-4 T

b)

earth magnetic feild , B1 = 0.5 uT = 5 * 10^-7 T

so, B = (1.26 * 10^-4 T) /( 5 * 10^-7) B1

B = 252 * B1

refrigerator magnetic feild , B2 = 0.5 mT = 5 * 10^-3 T

so, B = (1.26 * 10^-4 T) /( 5 * 10^-3) B2

B = 0.0252 * B2

MRIs magnetic feild , B3 = 1 u

so, B = (1.26 * 10^-4 T) /( 1) B3

B = 1.26 * 10^-4 * B3

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