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Q21P

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Fundamentals Of Physics
Found in: Page 858

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Illustration

Short Answer

Figure 29-49 shows two very long straight wires (in cross section) that each carry a current of4.00 A directly out of the page. Distance d1= 6.00 m and distance d2=4.00 m. What is the magnitude of the net magnetic field at point P, which lies on a perpendicular bisector to the wires?

Magnitude of the net magnetic field at point P is 256 nT.

See the step by step solution

Step by Step Solution

Given

  1. Permeability of free space, μ0=4π×10-7 TmA.
  2. d1=6.00 m.
  3. d2=4.00 m.
  4. Current carried by wire, i=4.00 A.

Understanding the concept

By using the concept of magnetic field due to long wire carrying current and component of magnetic field, determine the net magnetic field at point P.

Formula:

Magnetic field due to the wire at point P is

B=μ0i2πr

Here, i = current , μ0=permeability of free space, r = distance of wire.

Calculate the magnitude of the net magnetic field at point P.

First of all, we have to find the r.

By using Pythagoras theorem, solve as:

r=d122+d22

r=622+42

r=25r=5.00 m

Now, the magnetic field is given by

B=μ0i2πr

B=4π×10-7×4.02×3.14×5.00

B=1.6×10-7 T

B=160 nT

The component of the magnetic field cancels with each other, so the magnetic field at point P is

Bp=2 B sinθ

Here,

sinθ=d2r=4.005.00=0.8

Bp=2×160×0.8

Bp=256 nT

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