Question

In a long straight conductor carrying current, if the current is tripled and the distance of the point from the conductor is doubled, then the ratio of new magnetic induction to old magnetic induction is ______

• A. $3:2$
• B. $2:3$
• C. $4:9$
• D. $9:4$

Answer 1

The correct option is A $3:2$

Initial case,

current =I

Distance of the point =R

New case,

Current = 3I

Distance = 2R

${\overrightarrow{B}}_{initial}=\frac{{\mu }_{0}I}{4\pi R}$

${\overrightarrow{B}}_{final}=\frac{{\mu }_0\left(3I\right)}{4\pi \left(2R\right)}$

Now

$\frac{{\overrightarrow{B}}_{final}}{{\overrightarrow{B}}_{initial}}=\left(\frac{{\mu }_{0}3I}{4\pi \left(2R\right)}\right)/\left(\frac{{\mu }_{0}I}{4\pi R}\right)$

$3:2$