Statement-1 Magnetic field inside an ideal solonoid is uniform
Statement-2 Magnetic field outside an ideal solonoid is zero
Statement-3 Magnetic field at centre of an ideal solonoid is twice the magnetic field at the ends

Options

A. TTT
B. TTF
C. FFF
D. FFT

Answer

To analyze the three statements regarding the magnetic field in an ideal solenoid, we will evaluate each statement step by step.

### Step 1: Evaluate Statement 1
**Statement 1:** Magnetic field inside an ideal solenoid is uniform.

- An ideal solenoid is a long coil of wire with many turns. When a current flows through it, the magnetic field inside the solenoid is given by the formula:
\[ B = \mu_0 n I \]
where \( \mu_0 \) is the permeability of free space, \( n \) is the number of turns per unit length, and \( I \) is the current flowing through the solenoid.
- This formula indicates that the magnetic field \( B \) is constant (uniform) throughout the length of the solenoid, provided that the solenoid is long enough and the current is steady.

**Conclusion for Statement 1:** True.

### Step 2: Evaluate Statement 2
**Statement 2:** Magnetic field outside an ideal solenoid is zero.

- According to Ampere's circuital law, the magnetic field \( B \) around a closed loop is related to the current enclosed by that loop:
\[ \oint B \cdot dl = \mu_0 I_{\text{enclosed}} \]
- Outside the solenoid, there are no currents enclosed by an Amperian loop, which means \( I_{\text{enclosed}} = 0 \). Therefore, the magnetic field \( B \) outside the solenoid is:
\[ B = 0 \]

**Conclusion for Statement 2:** True.

### Step 3: Evaluate Statement 3
**Statement 3:** Magnetic field at the center of an ideal solenoid is twice the magnetic field at the ends.

- The magnetic field at the center of the solenoid \( B_C \) is given by:
\[ B_C = \mu_0 n I \]
- The magnetic field at the ends of the solenoid \( B_E \) is given by:
\[ B_E = \frac{\mu_0 n I}{2} \]
- From these equations, we can see that:
\[ B_C = 2 \times B_E \]
- This means that the magnetic field at the center of the solenoid is indeed twice that at the ends.

**Conclusion for Statement 3:** True.

### Final Conclusion
All three statements are true. Therefore, the correct option is:
- Option A: True, True, True.

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