A +3.75-HC point charge is moving at a constant 9.00 x 106 m/s in the +y-directi

Question

A +3.75-HC point charge is moving at a constant 9.00 x 106 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 =-0.300 m, y = 0, z = 0 magnitude -37.5 direction -x-direction (b) x = 0, y = +0.300 m, z = 0 magnitude directionSelect--- (c) x = 0, y = 0, z =-0.300 m magnitude direction -Select (d) x = 0, y = +0.300 m, z =-0.300 m magnitudee direction -Select

Explanation / Answer

magnetic field due to a point charge B = (uo*q/4pi)*(v x r)/r^3

(a)

r = -0.3 i

v = 9*10^6 j

q = 3.75*10^-6 C

magnitude of r = lrl = 0.3 m

B = (4*pi*10^-7*3.75*10^-6/(4*pi))*(9*10^6 j x -0.3 i)/0.3^3

B = (4*pi*10^-7*3.75*10^-6/(4*pi))*((9*10^6*0.3)/0.3^3) k

B = 3.75*10^-5 k T

magnitude = 3.75*10^-5

direction = +z direction

--------------------------------

(b)

r = xi + yj + zk = 0.3 j

v = 9*10^6 j

q = 3.75*10^-6 C

magnitude of r = lrl = 0.3 m

B = (4*pi*10^-7*3.75*10^-6/(4*pi))*(9*10^6 j x 0.3 j)/0.3^3

B = 0

magnitude = 0

direction = no direction

------------------------------

(c)

r = xi + yj + zk = -0.3 k

v = 9*10^6 j

q = 3.75*10^-6 C

magnitude of r = lrl = 0.3 m

B = -(4*pi*10^-7*3.75*10^-6/(4*pi))*(9*10^6 j x 0.3 k)/0.3^3

B = -(4*pi*10^-7*3.75*10^-6/(4*pi))*((9*10^6*0.3)/0.3^3) i

magnitude = 3.75*10^-5 T

direction = -x axis

========================

(d)

r = xi + yj + zk = 0.3 j - 0.3 k

v = 9*10^6 j

q = 3.75*10^-6 C

magnitude of r = lrl = sqrt(0.3^2+0.3^2) = 0.424 m

B = (4*pi*10^-7*3.75*10^-6/(4*pi))*(9*10^6 j x ( 0.3 j - 0.3 k))/0.424^3

B = -(4*pi*10^-7*3.75*10^-6/(4*pi))*((9*10^6*0.3)/0.424^3) i

magnitude = 1.33*10^-5 T

direction = -x axis

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