A pair of point charges, q = 7.8 ?C and q\' = -5.9 ?C, are moving as shown in th

Question

A pair of point charges, q = 7.8 ?C and q' = -5.9 ?C, are moving as shown in the figure above with speeds v = 6.3 x 104 m/s and v' = 6.7 x 104 m/s. The charges are at the locations shown in the figure.

A.What is the magnitude of the magnetic field at the origin?
(include units with answer)

B.What is the magnitude of the magnetic force that q' exerts on q?
(include units with answer)

C.What is the direction of the magnetic force that q' exerts on q? (CCW from +x direction)
(include units with answer)

Explanation / Answer

Bnet at Origin = Bnet = B1 + B2

each B due to Moving charge = (uo/4pi) (qVsin theta/r^2)

here theta = 90 deg

so

B1 = (2 e -7 * 7.8 e -6 * 6.3 e 4)/(0.309^2) = 1.029 uT

B2 = (2 e -7 * 5.9 e -6 * 6.7 e 4)/(0.361^2) = 0.606 uT

Bnet = 1.-29 - 0.606 = 0.423 uT

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

part B :

magnetic Force F = qvB

F = 7.8 e -6 * 6.3 e 4 * 0.423 e -6

F = 2.07 e -7 N

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

Directio tan theta = B2/B1

tan theta = 1.029/0.606 = 1.698

theta = 59.50 deg

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