5.19 A telephone cable at a place has four long straight horizontal wires carrying a current of 1.0 A in the same direction east to west. The earth’s magnetic field at the place is 0.39 G, and the angle of dip is 35 \degree. The magnetic declination is nearly zero. What are the resultant magnetic fields at points 4.0 cm below the cable?

Answers (1)
S safeer

Number of long straight horizontal wires = 4

The current carried by each wire = 1A

 earth’s magnetic field at the place = 0.39 G

the angle of dip = 350

magnetic field due to infinite current-carrying straight wire

B'=\frac{\mu_0I}{2\pi r}

r=4cm =0.04 m

B'=\frac{4\pi\times10^{-7}\times1}{2\pi \times4\times10^{-2}}

magnetic field due to such 4 wires

B=4\times \frac{4\pi\times10^{-7}\times1}{2\pi \times4\times10^{-2}}=2\times10^{-5}T

The horizontal component of the earth's magnetic field

H=0.39\times10^{-4}cos35=0.319\times10^{-4}T=3.19\times10^{-5}T

the horizontal component of the earth's magnetic field

V=0.39\times10^{-4}sin35=0.22\times10^{-4}T=2.2\times10^{-5}T

At the point below the cable

H'=H-B=3.19\times10^{-5}-2\times10^{-5}=1.19\times10^{-5}T

The resulting field is

\sqrt{H'^2+V^2}=\sqrt{(1.19\times10^{-5})^2+(2.2\times10^{-5})^2}=2.5\times10^{-5}T=0.25G

 

Preparation Products

Knockout NEET May 2021 (One Month)

An exhaustive E-learning program for the complete preparation of NEET..

₹ 14000/- ₹ 6999/-
Buy Now
Foundation 2021 Class 10th Maths

Master Maths with "Foundation course for class 10th" -AI Enabled Personalized Coaching -200+ Video lectures -Chapter-wise tests.

₹ 350/- ₹ 112/-
Buy Now
Foundation 2021 Class 9th Maths

Master Maths with "Foundation course for class 9th" -AI Enabled Personalized Coaching -200+ Video lectures -Chapter-wise tests.

₹ 350/- ₹ 112/-
Buy Now
Knockout JEE Main April 2021 (One Month)

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 14000/- ₹ 6999/-
Buy Now
Knockout NEET May 2021

An exhaustive E-learning program for the complete preparation of NEET..

₹ 22999/- ₹ 14999/-
Buy Now
Boost your Preparation for JEE Main with our Foundation Course
 
Exams
Articles
Questions