In a sketch of an evacuated tube

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Electricity, Magnetism & Electromagnetism · Vector calculus and field geometry

Electricity, Magnetism and Electromagnetism, Ch The Biot-Savart law and the fields of steady currents

Problem

In a sketch of an evacuated tube, one arrow shows the velocity of an electron: it lies in the

xz

-plane, has magnitude

2.0\times10^{6}\,\mathrm{m\,s^{-1}}

and points at

40^\circ

above the

+x

axis, turned towards

+z

. A second arrow shows a uniform magnetic field of magnitude

0.15\,\mathrm{T}

along

+\hat{\mathbf{y}}

. The electron has charge

-e

; gravity is ignored. ((a)) Write

\mathbf{v}

and

\mathbf{B}

in components. ((b)) Evaluate

\mathbf{v}\times\mathbf{B}

in components. ((c)) Give the magnetic force

\mathbf{F} = q\mathbf{v}\times\mathbf{B}

on the electron in components and its magnitude, and say which plane it lies in.

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