Q9. A rod is bent into a semi-circular shape with a radius of 0.5 m. A coil of 1500 turns carrying a current of 2A is wrapped uniformly around it. Describe the magnetic field's shape in this partial toroid.

Background

Topic: Magnetic Fields in Toroidal Solenoids (Toroids)

This question tests your understanding of how the magnetic field is distributed inside a toroidal solenoid, especially when the toroid is only partially formed (semi-circular). It also checks your ability to visualize the direction and shape of the magnetic field lines based on the current and coil arrangement.

Key Terms and Formulas

• Toroidal Solenoid: A coil shaped like a donut (or a ring), where the magnetic field is mostly confined within the core.

• Magnetic Field Direction: Determined by the right-hand rule for coils: if you curl your fingers in the direction of the current, your thumb points in the direction of the magnetic field inside the coil.

• Magnetic Field Strength (inside a toroid):

• = magnetic field strength

• = permeability of free space ( T·m/A)

• = number of turns

• = current

• = radius of the toroid

Step-by-Step Guidance

1. Visualize the semi-circular coil: The coil is wrapped uniformly around a half-circle, so the magnetic field will be concentrated inside the arc.

2. Apply the right-hand rule: Point your thumb in the direction of the current flow through the coil. Curl your fingers around the coil; the direction your fingers curl indicates the direction of the magnetic field inside the coil.

3. Recognize that the field lines will follow the arc: In a full toroid, the field lines form closed loops inside the core. In a semi-circular toroid, the field lines will follow the curve of the arc, pointing from one end to the other along the inside of the coil.

4. Compare the provided diagrams: Look for the image that shows the magnetic field lines concentrated inside the semi-circular coil, following the arc, and pointing in the direction determined by the right-hand rule.

Try solving on your own before revealing the answer!