Uniform magnetic field B is directed vertically upwards and 3 wires of equal length L , carrying equal current i are lying in a horizontal plane such that the first one is along north, second one along north–east and the third one at `60^(@)` north of east. Force exerted by magnetic field B on them is

Options

A. Zero on the first
B. `("BiL")/(sqrt2)` on the second
C. `sqrt3 "" ("BiL")/(2)` on the third
D. BiL on all of them

Explanation

To solve the problem, we need to calculate the force exerted by a uniform magnetic field on three wires carrying equal currents and positioned at different angles. The magnetic field is directed vertically upwards.

### Step-by-Step Solution:

1. **Understand the Configuration**:
- We have three wires of equal length \(L\) carrying equal current \(I\).
- The first wire is oriented along the North direction.
- The second wire is oriented along the North-East direction (45 degrees from North).
- The third wire is oriented at 60 degrees North of East.

2. **Magnetic Force Formula**:
- The force \(F\) on a current-carrying wire in a magnetic field is given by the formula:
\[ F = I \cdot L \cdot B \cdot \sin(\theta) \]
where \(I\) is the current, \(L\) is the length of the wire, \(B\) is the magnetic field strength, and \(\theta\) is the angle between the direction of the current and the magnetic field.

3. **Determine the Angle \(\theta\)**:
- For the first wire (North):
- The angle \(\theta\) is 90 degrees (since the magnetic field is vertical and the wire is horizontal).
- Thus, \(\sin(90^\circ) = 1\).
- Force \(F_1 = I \cdot L \cdot B \cdot 1 = I \cdot L \cdot B\).

- For the second wire (North-East):
- The angle \(\theta\) is also 90 degrees.
- Thus, \(\sin(90^\circ) = 1\).
- Force \(F_2 = I \cdot L \cdot B \cdot 1 = I \cdot L \cdot B\).

- For the third wire (60 degrees North of East):
- The angle \(\theta\) is also 90 degrees.
- Thus, \(\sin(90^\circ) = 1\).
- Force \(F_3 = I \cdot L \cdot B \cdot 1 = I \cdot L \cdot B\).

4. **Conclusion**:
- The magnitude of the force exerted by the magnetic field on each of the three wires is the same:
\[ F_1 = F_2 = F_3 = I \cdot L \cdot B \]

### Final Answer:
The force exerted by the magnetic field \(B\) on each of the three wires is \(I \cdot L \cdot B\).