Solveeit Logo
Login

Question

Question: Two infinite length wires carries currents 8A and 6A respectively and placed along X and Y-axis. Mag...

Two infinite length wires carries currents 8A and 6A respectively and placed along X and Y-axis. Magnetic field at a point P(0,0,d)mP ( 0,0 , d ) m will be

A

7μ0πd\frac { 7 \mu _ { 0 } } { \pi \mathrm { d } }

B
C

14μ0πd\frac { 14 \mu _ { 0 } } { \pi \mathrm { d } }

D
Answer
Explanation

Solution

Magnetic field at P

Due to wire 1, B1=μ04π⋅2(8)dB _ { 1 } = \frac { \mu _ { 0 } } { 4 \pi } \cdot \frac { 2 ( 8 ) } { d }

and due to wire 2, B2=μ04π⋅2(16)dB _ { 2 } = \frac { \mu _ { 0 } } { 4 \pi } \cdot \frac { 2 ( 16 ) } { d }

∴ Bnet=B12+B22=(μ04π⋅16d)2+(μ04π⋅12d)2B _ { n e t } = \sqrt { B _ { 1 } ^ { 2 } + B _ { 2 } ^ { 2 } } = \sqrt { \left( \frac { \mu _ { 0 } } { 4 \pi } \cdot \frac { 16 } { d } \right) ^ { 2 } + \left( \frac { \mu _ { 0 } } { 4 \pi } \cdot \frac { 12 } { d } \right) ^ { 2 } }

=μ04π×2d×10=5μ0πd= \frac { \mu _ { 0 } } { 4 \pi } \times \frac { 2 } { d } \times 10 = \frac { 5 \mu _ { 0 } } { \pi d }