An electron and a proton are each moving at 845 in perpendicular paths as shown in the figure

(Figure 1) .

At the instant they are at the positions shown in the figure. (A)

Find the magnitude of the total magnetic field they produce at the

origin.(B) Find the direction of the total magnetic field they

produce at the origin. (C) Find the magnitude of the magnetic field

the electron produces at the location of the proton. (D)Find the

direction of the magnetic field the electron produces at the

location of the proton.(E) Find the magnitude of the total magnetic

force that the electron exerts on the proton.(F) Find the direction

of the total magnetic force that the electron exerts on the

proton.(G) Find the magnitude of the total electrical force that

the electron exerts on the proton. (H) Find the direction of the

total electrical force that the electron exerts on the proton

counter clockwise from the positive x axis.

## Answer

(A) To find the magnitude of the total magnetic field they produce at the origin. B -B,+B 4x10x1.602x101x845x101 (5×109 (4×109 B: 1.39% 10% T (B) To find the direction of the total magnetic field they produce at the origin. The direction of the total magnetic field produced at the origin will be into the page.

(C) To find the magnitude of the magnetic field the electron produces at the location of the proton. Consider the formula, B–xqv sin θ r=15×10°)’ +(4×10-9) V25+16)x101 41 10 180-tan-1 θ 128.659 4MX 10-7×1 .602x 10-19x845x10%sin (128.659) B- 441 10 B= 2.578×10-4 T (D) To find the direction of the magnetic field the electron produces at the location of the protoin The direction of the magnetic field the electron produced at the location of the proton is into the page.

(E) To find the magnitude of the total magnetic force that the electron exerts on the mag -1.602×10.»,845x 103×2.58x 104 -3.492×10″N (F) To find the direction of the total magnetic force that the electron exerts on the proton. The direction of the total magnetic force that the electron exerts on the proton will be in the +x direction.

(G) To find the magnitude of the total electrical force that the electron exerts on the proton 1.602×1019 4Tx8.854x1041x104 -12 F5.625x10N (H) To find the direction of the total electrical force that the electron exerts on the proton counter clockwise from the positive x axis. The direction of the total electrical force that the electron exerts on the proton counter clockwise from the positive x axis is given by θ=360-51.341 θ-308.659