Question

A straight wire of diameter 0.5 mm carrying a current of 1 A is replaced by the another wire of 1 mm diameter carrying the same current. The strength of the magnetic field far away is

• A. one-quarter of the earlier value
• B. one-half of the earlier value
• C. twice the earlier value
• D. same as the earlier value

Answer 1

Answer: (D)

same as the earlier value

Answer 2

Diameter of first wire $(d_1)$ = 0.5 mm;
Current in first wire$(I_1)$ = 1A; Diameter of second
wire $(d_2) = 1$ mm and current in second wire $(I_2) = 1 A.$
Strength of magnetic field due to current flowing
in a conductor, $(B) = \frac{{\mu}_0}{4 \pi } \times \frac{2I}{ a} \, \, or \, \, B \propto I$
Since the current in both the wires is same,
therefore there is no change in the strength of the
magnetic field.