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Two magnetic fields exits in the two reg...

Two magnetic fields exits in the two regions as shown in . A loop abcd of `40 xx 10 cm` id placed in the field. The resistance per unit length of the loop is `r = 2Omegacm^(-1)`. All of a sudden, the loop is given a velocity `v_(0) = 20cm s^(-1)` towards roght. What is the potential difference `V_(c ) - V_(b)` ?

Text Solution

Verified by Experts

Given situation can be expressed by the following circuit diagram

`E_(1) = B_(1)lv_(0) = 3 xx 10^(2) xx 0.10 xx 0.20 = 6v`
`E_(2) = B_(2)lv_(0) = 2 xx 10^(2) xx 0.10 xx 0.20 = 4v`
`r_(1) = 2 xx 10 = 20 Omega`
`r_(2) = 2 xx 10 = 20 Omega`
Total resistance of the loop
`R = 2 xx 100 = 200 Omega`
Current through the circuit
`I = (E_(1) + E_(2))/(R) = (10)/(200) = 0.50 A`
`V_(c ) - V_(b) = -E_(2) + Ir_(2) = -4 + 0.05 xx 20 = -3 V`
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