Explanation Given info: The current flowing in wire 1 is 3.0 A pointing into the page, the current flowing in wire 2 is 4.0 A pointing out of the page and the distance of point P from wire 1 is 5.0 cm . Explanation: The diagram for the wire 1 and wire 2 at the corner S and R is given below. Figure (1) Formula to calculate magnetic field in vector form due to wire 1, B → 1 = μ o I 1 2 π r 1 ( x ^ ) Here, μ o is the permittivity of the free space. I 1 is the current flowing in wire 1. r 1 is the distance of wire 1 from point P. Substitute 4 π × 10 − 7 T ⋅ m / A for μ o , 3.0 A for I 1 , 5.0 cm for r 1 in above equation. B → 1 = ( 4 π × 10 − 7 T ⋅ m / A ) ( 3.0 A ) 2 π ( 5.0 cm ) ( x ^ ) = ( 4 π × 10 − 7 T ⋅ m / A ) ( 3.0 A ) 2 π ( 5.0 cm ( 10 − 2 m 1 cm ) ) ( x ^ ) = 1.2 × 10 − 5 T ( x ^ ) Formula to calculate magnetic field due to wire 2 at point P, B 2 → = μ o I 2 2 π r 2 [ cos θ ( − x ^ ) + sin θ ( y ^ ) ] (1) Here, I 2 is the current flowing in wire 2. r 2 is the distance of point P from wire 2. θ is the direction of point P from wire 2. Write the expression to calculate hypotenuse PR or r 2 triangle PSR. r 2 = PS 2 + SR 2 Here, SR is the base of triangle PSR. PS is the perpendicular of the triangle PSR. Substitute 5 cm for PS and 5 cm for SR in above equation. r 2 = ( 5 cm ) 2 + ( 5 cm ) 2 = ( 5 cm ( 10 − 2 m 1 cm ) ) 2 + ( 5 cm ( 10 − 2 m 1 cm ) ) 2 = 0.07 m Write the expression to calculate cosine of θ from the figure (1). cos θ = RS PR Here, PR is the hypotenuse of triangle PSR. Substitute 5 cm for RS and 0.7 m for PR in above equation. cos θ = ( 5 cm 0.07 m ) = ( 5 cm ( 10 − 2 m 1 cm ) ( 0.07 m ) ) = 0.71 Write the expression to calculate sine of θ from the figure (1). sin θ = PS P R Substitute 5 cm for PS and 0.7 m for PR in above equation. sin θ = ( 5 cm 0.07 m ) = ( 5 cm ( 10 − 2 m 1 cm ) ( 0.07 m ) ) = 0.71 Substitute 0.71 for cos θ , 0.71 for sin θ , 0.07 m for r 2 and 4

5th Edition

ISBN: 8220103026918

Author: Walker

Publisher: PEARSON

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Magnetic Force

A magnetic force arises when a charged particle or a current-carrying conductor is placed in a magnetic field. It is created because of the movement of the charged particles.

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Chapter 22, Problem 51PCE

To determine

The magnitude and direction of net magnetic field at point P.

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