(a) Explanation Given Info : The point charge ( q ) is + 6.00 μC , and the velocity towards the + y direction ( v → ) is 8.00 × 10 6 m / s . Formula to calculate the magnetic field vector is, B → = μ 0 4 π q v ^ × r ^ r 2 (I) μ 0 is the magnetic constant, q is the charge, v → is the velocity, r ^ is the unit vector from the point charge toward the magnetic field, r is the distance between the point charge to the magnetic field. Formula to determine the unit vector is, r ^ = r → r r → is the vector from the point charge to the field point, r is the magnitude of the unit vector. Formula to calculate the vector r → is r → = x i ^ + y j ^ + z k ^ Substitute 0.500 m for x , 0 for y , and 0 for z to find r → , r → = ( 0.500 m ) i ^ + ( 0 m ) j ^ + ( 0 m ) k ^ = ( 0.500 m ) i ^ Formula to calculate magnitude of the unit vector ( r ) is r = x 2 + y 2 + z 2 Substitute 0.500 m for x , 0 m for y , and 0 m for z to find r , r = ( 0.500 m ) 2 + ( 0 m ) 2 + ( 0 m ) 2 = 0.500 m The velocity of the charge acts in the + y direction at point x = 0.500 m . v → × r → = ( v j ^ ) ( 0.500 m ) i ^ = v ( 0.500 m ) ( j ^ × i ^ ) Substitute − k ^ for j ^ × i ^ and r for 0.500 m to find v → × r → , v → × r → = − v r k ^ Substitute r → r for r ^ and − v r k ^ for v → × r → in equation (I) to find B → (b) To determine The magnetic field vector B → at point x = 0 m , y = − 0.500 m , z = 0 (c) To determine The magnetic field vector B → at point x = 0 m , y = 0 m , z = + 0.500 m . (d) To determine The magnetic field vector B → at point x = 0 m , y = − 0.500 m , z = + 0.500 m .

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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.

Question

Chapter 28, Problem 28.1E

(a)

To determine

The magnetic field vector B→ at point x=0.500 m , y=0 , z=0 .

(b)

To determine

The magnetic field vector B→ at point x=0 m , y=−0.500 m , z=0

(c)

To determine

The magnetic field vector B→ at point x=0 m , y=0 m , z=+0.500 m .

(d)

To determine

The magnetic field vector B→ at point x=0 m , y=−0.500 m , z=+0.500 m .

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Chapter 28, Problem 28.20DQ

Chapter 28, Problem 28.2E

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The magnetic field vector B → at point x = 0.500 m , y = 0 , z = 0 .

Solution Summary: The author explains how the magnetic field vector stackreltoB is calculated.

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The magnetic field vector B→ at point x=0.500 m , y=0 , z=0 .

The magnetic field vector B→ at point x=0 m , y=−0.500 m , z=0

The magnetic field vector B→ at point x=0 m , y=0 m , z=+0.500 m .

The magnetic field vector B→ at point x=0 m , y=−0.500 m , z=+0.500 m .

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