Chapter 35

# Chapter 35 - 35.1. Model: Apply the Galilean transformation...

This preview shows pages 1–7. Sign up to view the full content.

35.1. Model: Apply the Galilean transformation of velocity. Solve: (a) In the laboratory frame S, the speed of the proton is () 22 66 6 1.41 10 m/s 2.0 10 m/s v + × = × The angle the velocity vector makes with the positive y -axis is 6 1 6 tan 45 θ ⎛⎞ × = ⎜⎟ × ⎝⎠ (b) In the rocket frame S , we need to first determine the vector v G . Equation 34.1 yields: ( ) ( ) 6 ˆˆ ˆ 1.41 10 1.41 10 m/s 1.00 10 m/s 0.41 10 1.41 10 m/s vvV i j i i j =−= × + × × = × + × G GG The speed of the proton is 666 0.41 10 m/s 1.47 10 m/s v + × = × The angle the velocity vector makes with the positive y -axis is 6 1 6 tan 16.2 × ′ = ×

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
35.2. Model: Apply the Galilean transformation of fields. Visualize: Please refer to Figure EX35.2. Solve: (a) Equation 35.11 gives the Galilean field transformation equation for magnetic fields: 2 1 B BV E c ′ = −× G GG G B G is in the positive ˆ k direction, ˆ B Bk = G . For B > B , VE × G G must be in the negative ˆ k direction. Since ˆ , E Ej = G V G must be in the negative ˆ i direction, so that ( ) ( ) ˆ ˆˆ . V E Vi Ej VEk ×= − × = G G The rocket scientist will measure B > B , if the rocket moves along the – x -axis. (b) For B = B , × must be zero. The rocket scientist will measure B = B if the rocket moves along either the + y -axis or the – y -axis. (c) For B < B , × must be in the positive ˆ k direction. The rocket scientist will measure B < B , if the rocket moves along the + x -axis.
35.3. Model: Use the Galilean transformation of fields. Solve: Equation 35.11 gives the Galilean transformation equations for the electric and magnetic fields in S and S frames: 2 1 E EVB B B VE c ′′ =+× =− × GGGG GG GG In a region of space where 0 B = G G , 6 ˆ 1.0 10 V/m. EE j == − × GG The magnetic field is () ( ) 12 66 5 2 2 8 11 . 0 1 0 ˆˆ 0 1.0 10 m/s 1.0 10 V/m T 1.11 10 T 3.0 10 B ij k k c × × ×− × = = × × G G

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
35.4. Model: Use the Galilean transformation of fields. Visualize: Please refer to Figure EX35.4. We are given 6 ˆ 2.0 10 m/s, Vi G ˆ 1.0 T, B j ′ = and 6 ˆ 1.0 10 V/m. Ek G Solve: Equation 35.11 gives the Galilean transformation equations for the electric and magnetic fields in S and S frames: 2 1 E EVB BB VE c ′′ =−× =+ × GGGG GG The electric and magnetic fields viewed from earth are ( ) ( ) ( ) 66 6 ˆˆ 1.0 10 V/m 2.0 10 m/s 1.0 T 1.0 10 V/m E ki j k − × × = G () 12 2 2 8 1 2.0 10 V/m ˆ ˆ ˆ ˆ 1.0 T 1.0 10 V/m 0.99998 T 3.0 10 m/s B ji k j j j c × =+ × × × = = × G Assess: Although , B B < you need 5 significant figures of accuracy to tell the difference between them.
35.5. Model: Use the Galilean transformation of fields. Visualize: Please refer to Figure EX35.5. We are given 6 ˆ 1.0 10 m/s, Vi G ˆ 0.50 T, B k = G and () 6 11 22 ˆˆ 10 V/m. Eij =+× G Solve: Equation 35.11 gives the Galilean transformation equation for the electric field in the S and S frames: E EVB GGGG . The electric field from the moving rocket is ( ) ( ) ( ) ( ) 66 6 6 ˆ ˆ ˆ ˆ 0.707 10 V/m 1.0 10 m/s 0.50 T 0.707 10 0.207 10 V/m Ei j i k i j =+ × + × × = × + × G 6 1 6 0.207 10 V/m tan 16.3 0.707 10 V/m θ ⎛⎞ × == ° ⎜⎟ × ⎝⎠ above the x -axis

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
35.6.
This is the end of the preview. Sign up to access the rest of the document.

## Chapter 35 - 35.1. Model: Apply the Galilean transformation...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online