The Definition of B — Question 9

Question 9

An acceleration component along the velocity reveals a nonmagnetic force

A particle has positive charge-to-mass ratio $q/m=2.00\times10^7$ C/kg, velocity $4.00\times10^4\hat x$ m/s and acceleration $(-2\hat x+3\hat y)10^6$ m/s squared.

1. Explain quantitatively why a magnetic field alone cannot produce this acceleration.

2. Assume the electric field has only an x component and the magnetic field only a z component. Determine both fields.

Question 9 - Solution

An acceleration component along the velocity reveals a nonmagnetic force

(a) Method and calculation

$$\vec a\cdot\vec v=(-2\times10^6)(4\times10^4)=-8.00\times10^{10}\,\mathrm{m^2/s^3}\ne0.$$$$\vec a_B\cdot\vec v=(q/m)(\vec v\times\vec B)\cdot\vec v=0.$$

(b) Interpretation and further calculation

$$a_x=(q/m)E_x\Rightarrow E_x=-.100\,\mathrm{V/m}.$$$$a_y=-(q/m)vB_z\Rightarrow B_z=-3.75\times10^{-6}\,\mathrm T.$$

Physical check

Only the electric component changes the speed at this instant under the stated field model.