兩條磁場計算(10分)

Question

(1)一根長2米的直導線,通有1安的電流,把它放在B=0.2特的勻強磁場中,當導線與磁力線的夾角為0°、30°和90°時,導線所受的安培力分別有多大?

(2)一個電子以1.2×107米/秒的速率射入B＝0.02特的勻強磁場中。當速度v與磁感強度B的夾角θ為30°和60°時，電子所受洛倫茲力分別是多大？

Answer 1

1. Let θ be the angle be the magnetic field lines and the straight conductor,
B be the flux density, I be the current in the conductor and L be the length of the conductor.

The force acting on the conductor F is:
F = B.L.I.sin(θ) = 0.2x2x1.sin(30) N (just take θ=30 deg. for example)
thus F = 0.2 N

substite the value of θ for other angles.

2. Let θ be the angle between v and B, then the Lorentz force F is given by:
F = q.v.B.sin(θ)
where q is the charge

when θ=30 deg. F = 1.6x10^-19x1.2x10^7x0.02.sin(30) N

use the the same equation to calculate θ=60 deg.