An electron experiences a magnetic force of the form qv times B. If the magnetic

Question

An electron experiences a magnetic force of the form qv times B. If the magnetic field has magnitude 0.1 Tesla and points in the z direction, and the electron is traveling due north at half the speed of light, give me the numerical value of the z component of acceleration. Consider two vectors a = x + y + z and b = x - y. Give me a vector that is perpendicular to both of them. In problem 1.17 on page 36 of Taylor's mechanics book he states the cross product rule for derivatives: d/dt (r times s) = r times ds/dt + dr/dt times s Use that rule to work out the derivative of angular momentum (defined as L = r times p. Explain very carefully why the derivative of angular momentum only has one term, not two, even though the cross product rule for derivatives has two terms.

Explanation / Answer

a) F = qv x B

z component of acceleration is zero as B is in z direction. So F will be perpendicular to z

b) vector c = a x b is perpendicular to both

= - z -z +y +x

= x +y - 2z

c) dL/dt = d(rxp)/dt = r x dp/dt + dr/dt xp

= r x F + 0xp

= r x F   

it is because radius or distance of force is constant

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