By how much is the approximation B = μonI [or in terms of 4πke Coulomb's constant ke, B = nI] in error at the center c² of a solenoid that is 10 cm long, has a diameter of 10 cm, is wrapped with n turns per meter, and carries a current I? Hint Compared to the exact expression, the approximation BonI is Select an answer by %.
By how much is the approximation B = μonI [or in terms of 4πke Coulomb's constant ke, B = nI] in error at the center c² of a solenoid that is 10 cm long, has a diameter of 10 cm, is wrapped with n turns per meter, and carries a current I? Hint Compared to the exact expression, the approximation BonI is Select an answer by %.
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![**Magnetic Field Approximation in a Solenoid**
**Question:**
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 10 cm long, has a diameter of 10 cm, is wrapped with \( n \) turns per meter, and carries a current \( I \)?
**Approach:**
- The question deals with understanding the error in the magnetic field approximation formulas.
- It's essential to recognize that the length (10 cm) and diameter (10 cm) of the solenoid, alongside the number of turns per meter \( n \) and the current \( I \), affect the calculation.
**Hint Button:**
- Click to get a hint for solving this problem.
**Calculation:**
Compared to the exact expression, the approximation \( B = \mu_0 n I \) is
\[ \text{Select an answer} \]
by _______%.
**Considerations:**
- Determine the exact magnetic field at the center of the solenoid.
- Compare it to the approximation provided.
**Note:**
- Ensure to examine the relative error in percentage to conclude the extent of discrepancy between the exact expression and the approximation.
Use interactive tools and additional resources on this website to enhance your understanding and solve related problems.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9bd1217a-91ba-44de-b552-38ea0e6629c6%2F3971bd29-33b5-4a55-81cb-bf18d63e59b7%2F5oru4he_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Magnetic Field Approximation in a Solenoid**
**Question:**
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 10 cm long, has a diameter of 10 cm, is wrapped with \( n \) turns per meter, and carries a current \( I \)?
**Approach:**
- The question deals with understanding the error in the magnetic field approximation formulas.
- It's essential to recognize that the length (10 cm) and diameter (10 cm) of the solenoid, alongside the number of turns per meter \( n \) and the current \( I \), affect the calculation.
**Hint Button:**
- Click to get a hint for solving this problem.
**Calculation:**
Compared to the exact expression, the approximation \( B = \mu_0 n I \) is
\[ \text{Select an answer} \]
by _______%.
**Considerations:**
- Determine the exact magnetic field at the center of the solenoid.
- Compare it to the approximation provided.
**Note:**
- Ensure to examine the relative error in percentage to conclude the extent of discrepancy between the exact expression and the approximation.
Use interactive tools and additional resources on this website to enhance your understanding and solve related problems.
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