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Chapter 4: Q70P (page 952)

The wire shown in Fig. P28.70 is infinitely long and carries a current l. Calculate the magnitude and direction of the magnetic field that this current

produces at point P

Short Answer

Expert verified

The magnitude and direction of the magnetic field that this current produces at point P is 渭0I4蟺aout of the page.

Step by step solution

01

Concept of Biot-Savart Law.

Biot-Savart Law in physics is a law in the form of a mathematical expression that describes the capability of a constant electric field to produce magnetic field.

Mathematically,

dB鈫�=渭04蟺Id鈦�I鈫�脳r^r2 鈥�.. (1)

Here, 渭0is the permeability of free space, dl鈫�is the length element, and r is the radius.

02

Determination of the magnitude and direction of the magnetic field that this current produces at point P.

For the horizontal line segment which gives a zero magnetic field, from equation (1) you can write,

dl鈫�脳r^=0

Magnetic field provided by the vertical segment is,

B=12渭0I2蟺a=渭0I4蟺a

Thus, the resultant magnetic field is渭0I4蟺aand is directed out of the page.

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