A rectangular loop has a sliding connector PQ of length $\ell$ and resistance $\mathrm { R } \Omega$ and it is moving with a speed $v$ as shown. The set-up is placed in a uniform magnetic field going into the plane of the paper. The three currents $I _ { 1 } , I _ { 2 }$ and $I$ are (1) $\mathrm { I } _ { 1 } = - \mathrm { I } _ { 2 } = \frac { \mathrm { B } \ell \mathrm { v } } { \mathrm { R } } , \mathrm { I } = \frac { 2 \mathrm {~B} \ell \mathrm { v } } { \mathrm { R } }$ (2) $\mathrm { I } _ { 1 } = \mathrm { I } _ { 2 } = \frac { \mathrm { B } \ell \mathrm { v } } { 3 \mathrm { R } } , \mathrm { I } = \frac { 2 \mathrm {~B} \ell \mathrm { v } } { 3 \mathrm { R } }$ (3) $I _ { 1 } = I _ { 2 } = I = \frac { B \ell v } { R }$ (4) $I _ { 1 } = I _ { 2 } = \frac { B \ell v } { 6 R } , I = \frac { B \ell v } { 3 R }$
A rectangular loop has a sliding connector PQ of length $\ell$ and resistance $\mathrm { R } \Omega$ and it is moving with a speed $v$ as shown. The set-up is placed in a uniform magnetic field going into the plane of the paper. The three currents $I _ { 1 } , I _ { 2 }$ and $I$ are\\
(1) $\mathrm { I } _ { 1 } = - \mathrm { I } _ { 2 } = \frac { \mathrm { B } \ell \mathrm { v } } { \mathrm { R } } , \mathrm { I } = \frac { 2 \mathrm {~B} \ell \mathrm { v } } { \mathrm { R } }$\\
(2) $\mathrm { I } _ { 1 } = \mathrm { I } _ { 2 } = \frac { \mathrm { B } \ell \mathrm { v } } { 3 \mathrm { R } } , \mathrm { I } = \frac { 2 \mathrm {~B} \ell \mathrm { v } } { 3 \mathrm { R } }$\\
(3) $I _ { 1 } = I _ { 2 } = I = \frac { B \ell v } { R }$\\
(4) $I _ { 1 } = I _ { 2 } = \frac { B \ell v } { 6 R } , I = \frac { B \ell v } { 3 R }$