**Transcription for Educational Website:**---**Magnetic Field Approximation in a Solenoid**By how much is the approximation \( B = \mu_0 n I \) [or in terms of Coulomb's constant \( k_e \), \( B = \frac{4 \pi k_e}{c^2} n I \)] in error at the center of a solenoid that is 24 cm long, has a diameter of 7 cm, is wrapped with \( n \) turns per meter, and carries a current \( I \)?**Hint**Compared to the exact expression, the approximation \( B = \mu_0 n I \) is:\[ \text{Select an answer } \ \_\_\_\ \% \]**Question Help:**

Given,The approximation B = μ0nIThe length of the solenoid, l = 24 cmThe diameter of the solenoid, d = 7 cmThe radius of the solenoid, r = d2= 3.5 cmnumber of turns per meter = nThe exact expression of Bexact = μ0nI1+4R2L2The difference, ∆ = B-BexactBexact∆ =μ0nI-μ0nI1+4R2L2μ0nI1+4R2L2=1+4R2L2-11The percentage difference, ∆%=1+4R2L2-1×100⇒∆%=1+4×(3.5)2(24)2-1×100=1+0.085-1×100⇒∆%=4.1%Compared to exact expression, the approximation B = μ0nI is greater thanby 4.1%

Answered: 4πke ke, B By how much is the…

4πke ke, B By how much is the approximation B HonI [or in terms of Coulomb's constant -nI] in error at the center of a solenoid that is 24 cm long, has a C² diameter of 7 cm, is wrapped with n turns per meter, and carries a current I? Hint