物理題目一問MC題(磁場強度')

MM2 89B_HH1412

2013-02-01 4:01 am

把一霍耳探測器放在一勻場強度內。該探測器內的半導體晶片厚 1.3x10^-3m，而每立方米有 10^25個載荷子。當 0.4A的穩恆電流通過晶片，產生的霍耳電壓為 2x10^-5V。探測器測得的磁場強度為多少？假設每個載荷子所帶電荷的量值為 1.6x10^-19C。

更新1:

A. 0.104T B. 0.962T C. 1.04T D. 9.62T Details, thanks.

回答 (1)

天同

2013-02-01 7:38 am

✔ 最佳答案

At steady state, the electric force and magnetic force acting on a charge carrier balance each other.
Hence, qE = Bqv
where q is the charge on each carrier
E is the electric field intensity
B is the magnetic field intensity
v is the charge drift velocity

But E = V/d
where V is the Hall voltage and d is the width of the semi-conductor slab
hence, qV/d = Bqv
V = Bdv

Since current I = nqvA
where n is the no. of charge carriers per unit volume
A is the cross-sectional area of the slab (= d.t, t is the slab thickness)
Thus, v = I/nqA = I/nqdt

The Hall voltage V = Bd.(I/nqdt) = B.I/nqt
i.e. B = Vnqt/I = (2x10^-5) x (10^25) x (1.6x10^-19) x (1.3x10^-3)/0.4 T
B = 0.104 T

The answer is option A

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