For a solenoid of length L, radius R, and carrying current I, what is the magnetic field inside the solenoid?
Practice Questions
1 question
Q1
For a solenoid of length L, radius R, and carrying current I, what is the magnetic field inside the solenoid?
μ₀nI
μ₀I/L
μ₀I/2L
μ₀I/4L
Using Ampere's Law, B = μ₀nI where n is the number of turns per unit length.
Questions & Step-by-step Solutions
1 item
Q
Q: For a solenoid of length L, radius R, and carrying current I, what is the magnetic field inside the solenoid?
Solution: Using Ampere's Law, B = μ₀nI where n is the number of turns per unit length.
Steps: 7
Step 1: Understand what a solenoid is. A solenoid is a coil of wire that creates a magnetic field when an electric current passes through it.
Step 2: Identify the parameters given in the question: length (L), radius (R), and current (I).
Step 3: Know that the magnetic field inside a long solenoid can be calculated using Ampere's Law.
Step 4: Recognize that Ampere's Law states that the magnetic field (B) inside a solenoid is proportional to the number of turns per unit length (n) and the current (I).
Step 5: Calculate the number of turns per unit length (n) by dividing the total number of turns (N) by the length (L) of the solenoid: n = N / L.
Step 6: Use the formula B = μ₀nI, where μ₀ is the permeability of free space (a constant).
Step 7: Substitute the value of n from Step 5 into the formula to find the magnetic field B inside the solenoid.
