- Current (I) = 10 A
- Radius of bent coil (r) = 3 cm


The formula to calculate the magnetic field at the center of a circular coil is given by:

B = (μ₀ * I * n) / (2 * r)

Where:
- B is the magnetic field at the center
- μ₀ is the permeability of free space (4π × 10⁻⁷ T m/A)
- I is the current flowing through the wire
- n is the number of turns in the coil
- r is the radius of the coil


- We are given the current (I) = 10 A
- The radius of the bent coil (r) = 3 cm = 0.03 m

To find the magnetic field at the center, we need to determine the number of turns in the coil (n).


- The number of turns in the coil can be determined by the angle of bending.
- Since the figure is not provided, we cannot directly determine the angle of bending.
- We will assume a complete circular coil and calculate the magnetic field using this assumption.
- In a complete circular coil, the angle of bending is 360° or 2π radians.
- The length of the wire in a complete circular coil is equal to the circumference of the circle.
- The circumference of a circle is given by the formula: C = 2πr
- Therefore, the length of the wire in a complete circular coil is 2πr.


- The length of wire used in the bent coil = 2πr
- As we know the length of wire used in a complete circular coil is 2πr.
- Therefore, the number of turns in the coil (n) = (2πr) / (2πr) = 1


- Substituting the given values into the formula:
- B = (μ₀ * I * n) / (2 * r)
- B = (4π × 10⁻⁷ T m/A) * (10 A) * (1) / (2 * 0.03 m)
- B = 2.67 × 10⁻⁴ T


The magnitude of the magnetic field at the center of the bent coil carrying a current of 10 A and with a radius of 3 cm is 2.67 × 10⁻⁴ T.