if the current in each wire is the same, which wire produces the strongest magnetic field?\n a wire that is…

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

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

Answer

Explanation:

Step1: Recall the formula for magnetic field of a solenoid

The magnetic field (B) of a solenoid (coiled wire) is given by (B = \mu_0nI), where (\mu_0) is the permeability of free space, (n) is the number of turns per unit length, and (I) is the current. For a straight wire (not coiled), the magnetic field (B=\frac{\mu_0I}{2\pi r}). When the wire is coiled (solenoid - like), the magnetic field is enhanced because of the additive effect of the magnetic fields from each loop.

Step2: Compare the options

  • For non - coiled wires (straight wires), the magnetic field is relatively small. The formula (B=\frac{\mu_0I}{2\pi r}) (where (r) is related to the wire's position in space, and thickness has a minor effect on the external magnetic field compared to coiling).
  • For coiled wires, the number of loops matters. A 1 - mm - thick coiled wire with ten loops has a higher number of loops (higher (n) in the solenoid formula (B = \mu_0nI)) compared to a 2 - mm - thick coiled wire with two loops. Since the current (I) is the same for all wires.

Answer:

a 1 - mm - thick coiled wire with ten loops