A particle with charge 6.00 nC is moving in a uniform magnetic field B =( 1.23 T

Question

A particle with charge 6.00 nC is moving in a uniform magnetic field B =( 1.23 T )k^. The magnetic force on the particle is measured to be F =( 3.50×107 N )i^+( 7.60×107 N )j^.

Part A

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

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Correct

Part B

Calculate the x-component of the velocity of the particle.

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Part C

Calculate the y-component of the velocity of the particle.

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Part D

Calculate the scalar product v F .

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Part E

What is the angle between v  and F ? Give your answer in degrees.

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A particle with charge 6.00 nC is moving in a uniform magnetic field B =( 1.23 T )k^. The magnetic force on the particle is measured to be F =( 3.50×107 N )i^+( 7.60×107 N )j^.

Part A

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

Are there components of the velocity that are not determined by the measurement of the force? yes no

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Correct

Part B

Calculate the x-component of the velocity of the particle.

vx =   m/s  

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Part C

Calculate the y-component of the velocity of the particle.

vy =   m/s  

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Part D

Calculate the scalar product v F .

v F  =   m/sN  

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Part E

What is the angle between v  and F ? Give your answer in degrees.

=     

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Explanation / Answer

q = - 6 nC, B = -1.23 k

F = -3.5*10^-7 i +7.6*10^-7 j

F = q(vxB)

-3.5*10^-7 i +7.6*10^-7 j = -6*10^-9 (vxi +vy j +vz k)(-1.23 k)

-3.5*10^-7 i +7.6*10^-7 j = (-6*10^-9*1.23*vx j + 6*10^-9*1.23*vy i)

Part B:

7.6*10^-7 = -6*10^-9*1.23*vx

vx = -103 m/s

-3.5*10^-7 = 6*10^-9*1.23*vy

vy = -47.4 m/s

Pat C: -3.5*10^-7 = 6*10^-9*1.23*vy

vy = -47.4 m/s

Part D: v.F = (-103 i -47.4 j) .(-3.5*10^-7 i +7.6*10^-7 j)

= (-103*-3.5*10^-7 -47.4*7.6*10^-7)

= 2.6*10^-8

Part E:

v.F = v*F*Cos(theta)

2.6*10^-8 = (103^2 +47.4^2)^0.5*10^-7(3.5^2 +7.6^2)^0.5*cos(theta)

theta = 89.98 degrees

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