Two identical coils are placed coaxially. They carry equal currents in same direction
NOTE in parts (a), (b) and (c) exclude the points at infinity.

Options

A. (a)on their axis there are two points where net magnetic field is zero
B. (b)on their axis there are three points where net magnetic field is zero
C. (c)on their axis there is no such point where net magnetic field is zero
D. (d)on moving from the centre of one coil to the other, magnetic field will first decrease then increase

Answer

To solve the problem of two identical coils placed coaxially carrying equal currents in the same direction, we will analyze the magnetic field created by these coils and determine if there are any points along the axis where the net magnetic field is zero.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have two identical coils placed one above the other, and they are coaxial.
- Both coils carry equal currents in the same direction.

2. **Direction of Magnetic Field**:
- According to the right-hand rule, if the current in both coils flows in the same direction (let's assume clockwise when viewed from one end), the magnetic field produced by each coil will also point in the same direction along the axis of the coils.
- Therefore, at any point along the axis of the coils, the magnetic fields due to both coils will be in the same direction.

3. **Analyzing Points Along the Axis**:
- The magnetic field due to a single coil at a point along its axis can be calculated using the formula:
\[ B = \frac{\mu_0 n I}{2R} \left(1 - \frac{z}{\sqrt{z^2 + R^2}}\right) \]
where \(B\) is the magnetic field, \(I\) is the current, \(R\) is the radius of the coil, \(z\) is the distance from the center of the coil along the axis, and \(n\) is the number of turns.
- For two coils, the total magnetic field at any point on the axis is simply the sum of the magnetic fields due to each coil.

4. **Finding Points of Zero Magnetic Field**:
- Since both coils produce magnetic fields in the same direction, the magnetic fields will add up at every point along the axis.
- Therefore, there cannot be a point along the axis where the magnetic fields from both coils cancel each other out.

5. **Conclusion**:
- Since the magnetic fields from both coils are always in the same direction and add up, there are no points along the axis where the net magnetic field is zero.
- Thus, the answer to the question is that there is no such point on the axis where the net magnetic field is zero.

### Final Answer:
There is no point on the axis where the magnetic field is zero.

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