https://file.aiquickdraw.com/mathbot/file/1729146489744jbg5tgi2.jpg

The question in the image is written in Indonesian, and it reads as follows:

**Translation:**
"A solenoid with a length of 50 cm consists of 1,500 turns. If the solenoid carries a current of 10 A, the magnetic induction at the center of the solenoid is?"

To solve this problem, we use the formula for the magnetic field \( B \) at the center of a solenoid:

\[
B = \mu_0 \cdot n \cdot I
\]

where:
- \( B \) is the magnetic induction (in Tesla),
- \( \mu_0 \) is the permeability of free space (\( 4\pi \times 10^{-7} \ \text{T} \cdot \text{m/A} \)),
- \( n \) is the number of turns per unit length (turns per meter),
- \( I \) is the current through the solenoid (in Amperes).

### Step 1: Calculate \( n \) (turns per unit length)
\[
n = \frac{N}{L}
\]
where:
- \( N = 1,500 \) turns,
- \( L = 50 \ \text{cm} = 0.5 \ \text{m} \).

Thus,
\[
n = \frac{1500}{0.5} = 3000 \ \text{turns/m}.
\]

### Step 2: Calculate the magnetic induction \( B \)
Now, plug in the values into the formula:
\[
B = (4\pi \times 10^{-7}) \times 3000 \times 10.
\]

Simplifying the expression:
\[
B = (4\pi \times 10^{-7}) \times 30,000.
\]

\[
B \approx 3.77 \times 10^{-2} \ \text{T} = 0.0377 \ \text{T}.
\]

Thus, the magnetic induction at the center of the solenoid is approximately **0.0377 Tesla**.

Would you like further explanation or details? Here are some related questions to explore this concept further:

1. What is the significance of the magnetic field inside a solenoid?
2. How does the number of turns per unit length affect the magnetic induction?
3. Why does the magnetic field at the center of the solenoid depend on the current?
4. How does the length of the solenoid influence the magnetic field it generates?
5. What happens to the magnetic induction if the solenoid's current is doubled?

**Tip:** Always ensure the solenoid is long enough so that edge effects don't significantly affect the magnetic field at its center.

A solenoid with a length of 50 cm consists of 1,500 turns. If the solenoid carries a current of 10 A, the magnetic induction at the center of the solenoid is?

Learn how to calculate the magnetic induction at the center of a solenoid with a length of 50 cm, 1,500 turns, and a current of 10 A. This problem covers key concepts in electromagnetism, including the magnetic field in a solenoid and the formula B = μ₀ * n * I. Suitable for students in Grades 10-12.

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