Question

Certain experiments must be performed in the absence of any magnetic fields. Suppose such an experiment is located at the center of a large solenoid oriented so that a current of I = 1.50 A produces a magnetic field that exactly cancels Earth's 4.50 ✕ 10−5 T magnetic field. Find the solenoid's number of turns per meter.

Answer 1

Answer- For the large solenoid magnetic field produced at the center is given by relation

n= N/L

N= turns , L= length of the solenoid

now given

B= 4.50 ✕ 10−5 T ,I=1.50 A

So the solenoid's number of turns per meter can be calculated as

n=B/μ₀ I

μ₀ = 4π×10⁻⁷ H/m ,B= 4.50 ✕ 10−5 T ,I=1.50 A

putting these values

n=4.50 ✕ 10−5 T/4π×10⁻⁷ H/m*1.50 A

n=24.03 turns per meter