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A metal strip6.50cm long, 0.850 cm wide, and 0.760 mm thick moves with constant velocity through a uniform magnetic field B=1.20mT directed perpendicular to the strip, as shown in Fig.12-34. A potential difference of 3.90μvis measured between points xand yacross the strip. Calculate the speed.

Short Answer

Expert verified

The speed of the metal strip isv=3.9μV10-81μv=3.9×10-6v v=0.382 m/s .

Step by step solution

01

Given

V=3.9‰ӼV10−6 V1‰ӼV=3.9×10-6 V

d=0.850 c³¾10−2″¾1 c³¾=8.50×10-3m

B=1.20 mT10-3T1 mT=1.20×10-3T

02

Determining the concept

If the strip is moving with constant velocity, then acceleration will be zero. So electric and magnetic forces will balance each other

Formulae are as follows:

Fe=qE

Fm=qvB

E=V/d

Where Feis electric force, Fm is a magnetic force,

v is velocity, E is the electric field, B is the magnetic field, q is the charge of the particle, and d is distance.

03

Determining the speed of the metal strip 

Here, both forces are in balance.

Hence,

Fm=Fe

qvB=qE

v=EB

v=VBd

v=3.9×10−6 V1.20×10−3 T×8.50×10−3 m=0.382 m/s

Hence, the speed of the metal strip is,v=0.382m/s.

Therefore, by using the formula of electric and magnetic forces, the velocity of the metal strip can be determined.

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