a current in a wire increases from 2 a to 6 a. how will the magnetic field 0.01 m from the wire change?\nit…

a current in a wire increases from 2 a to 6 a. how will the magnetic field 0.01 m from the wire change?\nit increases to four times its original value.\nit increases to three times its original value.\nit decreases to one - fourth its original value.\nit decreases to one - third its original value.

a current in a wire increases from 2 a to 6 a. how will the magnetic field 0.01 m from the wire change?\nit increases to four times its original value.\nit increases to three times its original value.\nit decreases to one - fourth its original value.\nit decreases to one - third its original value.

Answer

Explanation:

Step1: Recall magnetic - field formula

The magnetic - field formula for a long straight wire is $B=\frac{\mu_0I}{2\pi r}$, where $\mu_0 = 4\pi\times10^{-7}\ T\cdot m/A$, $I$ is the current, and $r$ is the distance from the wire. Let the initial current be $I_1 = 2A$ and the final current be $I_2=6A$, and the distance $r$ remains constant ($r = 0.01m$).

Step2: Calculate the ratio of final to initial magnetic fields

We know that $B_1=\frac{\mu_0I_1}{2\pi r}$ and $B_2=\frac{\mu_0I_2}{2\pi r}$. Then, $\frac{B_2}{B_1}=\frac{\frac{\mu_0I_2}{2\pi r}}{\frac{\mu_0I_1}{2\pi r}}=\frac{I_2}{I_1}$. Substitute $I_1 = 2A$ and $I_2 = 6A$ into the ratio: $\frac{B_2}{B_1}=\frac{6A}{2A}=3$.

Answer:

It increases to three times its original value.