Question

if the current in each wire is the same, which wire produces the strongest magnetic field?
o a wire that is 1 mm thick and not coiled
o a wire that is 2 mm thick and not coiled
o a 1 -mm -thick coiled wire with ten loops
o a 2 -mm -thick coiled wire with two loops

Explanation:

Step1: Recall magnetic - field formula for a wire

The magnetic field produced by a current - carrying wire is enhanced when the wire is coiled. The magnetic field of a solenoid (coiled wire) is given by $B=\mu_0 nI$, where $n$ is the number of turns per unit length and $I$ is the current. For a single - straight wire, the magnetic field at a distance $r$ from the wire is $B = \frac{\mu_0I}{2\pi r}$. Coiling the wire increases the magnetic field because the magnetic fields of each loop add up.

Step2: Compare the options

Among the given options, the coiled wires will produce a stronger magnetic field than the non - coiled wires. Comparing the coiled wires, the 1 - mm - thick coiled wire with ten loops has more loops than the 2 - mm - thick coiled wire with two loops. More loops mean a stronger magnetic field when the current is the same.

Answer:

a 1 - mm - thick coiled wire with ten loops