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A rectangular loop with a sliding connec...

A rectangular loop with a sliding connector of length `l` is located in a uniform magnetic field perpendicular to the loop plane. The magnetic induction is equal to B. The connector has an electric resistance `R`, the sides `ab` and `cd` have resistances `R_1` and `R_2`. Neglecting the self-inductance of the loop, find the current flowing in the connector during its motion with a constant velocity v.

Text Solution

Verified by Experts

The correct Answer is:
A, B
Motional emf `V=Bvl`
Net resistance of the circuit `=R+(R_1R_2)/(R_1+R_2)`
` :.` Current through the connector
`i=(Bvl)/(R+(R_(1)R_(2))/(R_(1)+R_(2)))`
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Knowledge Check

  • A rectangular loop with a sliding connector of length 10 cm is situated in uniform magnetic field perpendicular to plane of loop. The magnetic induction is 0.1 tesla and resistance of connector (R ) is 1 ohm . The sides AB and CD have resistances 2 ohm and 3 ohm respectively. Fibd the current in the connector during its motion with constant velocity one

    A
    `1/110A`
    B
    `1/220A`
    C
    `1/55A`
    D
    `1/440A`

  • A rectangular loop with a sliding conductor of length l is located in a uniform magnetic field perpendicular to the plane of the loop . The magneitc inducetion is b . The resistances R_(1) and R_(2) , respectively. Find the current through the conductor during its motion to the right with a constant velocity v .

    A
    (a) `(Blv(R_(1) + R_(2)))/(R_(1)(R_(1) + R_(2))`
    B
    (b) `(Bl^(2)v)/(R_(1) + R_(1) R_(2))`
    C
    ( c) `(Blv(R_(1) + R_(2)))/(R_(1)R_(2)+ R(R_(1) + R_(2))`
    D
    (d) `(Bl^(2)v)/(R_(1)R_(2) + R(R_(1) + R_(2))`

  • A rectangular loop with a sliding connector of length l=1.0 m is situated in a uniform magnetic field B=2T perpendicular to the plane of loop. Resistance of connector is r=2Omega .Two resistance of 6Omega and 3Omega are connector is r=2Omega . two resistance of 6Omega and 3Omega are connected as shown in figure. the external force required to keep the connector moving with a constant velocity v=2m//s is

    A
    `6N`
    B
    `4N`
    C
    `2N`
    D
    `1N`
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