Question

A +5.50 μC point charge is moving at a constant 8.00 ×106m/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 B⃗  it produces at the following points.

Part A

x=0.500m,y=0, z=0

Enter your answers component-wise and numerically separated by commas.

Bx, By, Bz =

__

  T  

Part B

x=0, y=−0.500m, z=0

Enter your answers component-wise and numerically separated by commas.

Bx, By, Bz = ___

  T  

Part C

x=0, y=0, z=+0.500m

Enter your answers component-wise and numerically separated by commas.

Bx, By, Bz =

___ T  

Part D

x=0, y=−0.500m, z=+0.500m

Enter your answers component-wise and numerically separated by commas.

Bx, By, Bz = ___

  T  

Answer 1

Magnetic field due to a moving charge,

B = uo*q (x) / 4r^3

(a)

At x = 0.50 m,

B = 4*10^-7*5.5*10^-6*(8*10⁶ j x 0.50 i) / 4*(0.50)^3

B = 1.76*10^-5 T (-k)

(Bx , By , Bz) = (0 , 0 , -1.76*10^-5 ) T

(b)

At y = -0.50 m

B = 4*10^-7*5.5*10^-6*(8*10⁶ j x -0.50 j) / 4*(0.50)^3

B = 0

(Bx , By , Bz) = (0 , 0 0) T

(c)

At z = 0.50 m,

B = 4*10^-7*5.5*10^-6*(8*10⁶ j x 0.50 k) / 4*(0.50)^3

B =  1.76*10^-5 T (i)

(Bx , By , Bz) = (1.76*10^-5 , 0 , 0) T

(d)

At y = −0.50 m , z = +0.50 m,

magnitude of the position vector, r = sqrt (0.50^2 + 0.50^2)

r = 0.707 m

B = 4*10^-7*5.5*10^-6*(8*10⁶ j x (-0.50 j + 0.50 k)) / 4*(0.707)^3

B = 0.62*10^-5 T (i)

(Bx , By , Bz) = (0.62*10^-5 , 0 , 0) T