Question

– A particle with charge -5.60 nC is moving in a uniform magnetic field ??? = ?(1.25 ??)???.

The magnetic force on the particle is measured to be ?? = ?(3.40 × 10?7 N)??? + (7.40 × 10?7 N)???.

(a) Calculate all the components of the velocity of the particle that you can from this information.

(b) Are there components of the velocity that are not determined by the measurement of the force?

Explain your answer. (c) Calculate the scalar product of ?? ? ?? . What is the angle between ?? and ?? ?

Answer 1

Let the velocity be Vxi +Vyj + Vzk

F = q(V X B)

10^-7*(-3.4i + 7.4j) = -5.6*10^-9* [ i j k ]

[Vx Vy Vz]

[0 0 -1.25]

17.85(-3.4i + 7.4j) = i(-1.25 Vy) - j(-1.25Vx) + k(0 - 0 )

Vy = (17.85 * -3.4 / -1.25) = 48.57

Vx = 105.67

V = 105.67 i + 48.57 j +Vzk

b) yes the z-componet of Velocity could nt be determined by Force

c) scalar product = (105.67).(-3.4*10^-7) + (48.57*7.4*10^-7)

= 7.18*10^-5

angle = cos^-1 ( 7.18*10^-5 / sqrt(105.67^2 + 48.57^2)*10^-7*sqrt(3.4^2 + 7.4^2) )

= 40.7^o