A +4.75-muC point charge is moving at a constant 6.15 times 10^6 m/s in the +y-d
ID: 1648676 • Letter: A
Question
A +4.75-muC point charge is moving at a constant 6.15 times 10^6 m/s in the +y-direction, relative to a reference frame. At the instant when the point charge is at the origin of this reference frame, what is the magnetic-field vector B it produces at the following points? (a) x= +0.375 m, y = 0, z = 0 (b) x = 0, y =-0.375 m, z = 0 (c) x = 0, y = 0, z = +0.375 m (d) x = 0, y =-0.375 m, z = +0.375 m Positive point charges q = +8.25 mu C and q' = +3.25 mu C are moving relative to an observer at point P, as shown in the following figure. The distance d is 0.160 m, v = 5.00 times 10^6 m/s, and v' = 8.60 times 10^6 m/s.Explanation / Answer
(a)
The magnetic field is
B = (u0/4*pi)*(q*v*r/r^3)
= (4*pi*10^-7/4*pi)*[(4.75*10^-6)*(6.15*10^6)*(0.375)/(0.375)^3]
= 2.077*10^-5 T
The magnitude of the magnetic field is 2.077*10^-5 T and the direction is along the negative z axis
(b)
The magnetic field is
B = (u0/4*pi)*(q*v*r/r^3)
= (4*pi*10^-7/4*pi)*[(4.75*10^-6)*(6.15*10^6)*(- 0.375)/(0.375)^3]
= 0 T
The magnitude of the magnetic field is 0 T
(c)
The magnetic field is
B = (u0/4*pi)*(q*v*r/r^3)
= (4*pi*10^-7/4*pi)*[(4.75*10^-6)*(6.15*10^6)*(0.375)/(0.375)]
= 2.077*10^-5 T
The magnitude of the magnetic field is 2.077*10^-5 T and the direction is along the positive x axis.
(d)
The magnetic field is
B = (u0/4*pi)*(q*v*r/r^3)
= (4*pi*10^-7/4*pi)*[(4.75*10^-6)*(6.15*10^6)*(0.375(-j) + 0.375 k)/sqroot(0.375^2
0.375^2)^3]
= 7.596*10^-6 T
The magnitude of the magnetic field is 7.596*10^-6 T and the direction is along the positive x axis.
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