Electronics Engineering (ELEX) Board Practice Exam

A length L of wire carries a steady current of 1 A. If it is bent to form a double loop, how does the magnetic field at the center compare to its first value?

1. It remains the same.

2. It doubles.

3. It quadruples.

4. It halves.

The correct answer is: It quadruples.

When a length of wire carrying a steady current is bent to form a loop, the magnetic field generated depends on the configuration of the loop. The magnetic field at the center of a single loop of wire carrying a current can be described using the formula: \[ B = \frac{\mu_0 I}{2r} \] where \( B \) is the magnetic field, \( \mu_0 \) is the permeability of free space, \( I \) is the current, and \( r \) is the radius of the loop. When the wire is bent into a double loop, it essentially forms two loops in close proximity to each other. The magnetic field at the center of the loops from each individual loop will add up due to the direction of the current flowing through both loops being the same. Specifically, if you have two loops, the magnetic fields generated by each loop combine constructively. Since the magnetic field generated by one loop is proportional to the number of loops (assuming all other factors remain constant, such as the length of wire and the current), the resulting magnetic field at the center of the double loop configuration is twice that of a single loop setup. However, when considering the arrangement of the wire more thoroughly, as