AB is a resistance less conducting rod which forms a diameter of a conducting ring of radius textr rotating in a uniform magnetic field textB as shown in the diagram. The resistors textR1 and textR2 do not rotate. Then the current through the resistor textR1 is

Question

AB is a resistance less conducting rod which forms a diameter of a conducting ring of radius textr rotating in a uniform magnetic field textB as shown in the diagram. The resistors textR1 and textR2 do not rotate. Then the current through the resistor textR1 is <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-dg3zt7evgkhxu5kx.jpg" /> (A) (B ω r2/2 R1) (B) (B ω r2/2 R2) (C) (B ω r2/2 R1 R2)(R1 + R2) (D) (B ω r2/2 (R1 + R2))

Tardigrade Admin · Accepted Answer

The equivalent diagram is <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-dg3zt7evgkhxhpxp.jpg" /> The induced emf across the centre and any point on the circumference is ϵ =(1/2)Bω ℓ 2=(B ω r2/2) &there4; Current through R1=(B ω r2/2 R1)

Q. $A B$ is a resistance less conducting rod which forms a diameter of a conducting ring of radius $r$ rotating in a uniform magnetic field $B$ as shown in the diagram. The resistors $R_{1}$ and $R_{2}$ do not rotate. Then the current through the resistor $R_{1}$ is

$\frac{B ω r ^{2}}{2 R _{1}}$

$\frac{B ω r ^{2}}{2 R _{2}}$

$\frac{B ω r ^{2}}{2 R _{1} R _{2}} (R_{1} + R_{2})$

$\frac{B ω r ^{2}}{2 ( R _{1} + R _{2} )}$

The equivalent diagram is

The induced emf across the centre and any point on the
circumference is
$ϵ = \frac{1}{2} B ω ℓ^{2} = \frac{B ω r ^{2}}{2}$
∴ Current through $R_{1} = \frac{B ω r ^{2}}{2 R _{1}}$

Q. AB is a resistance less conducting rod which forms a diameter of a conducting ring of radius r rotating in a uniform magnetic field B as shown in the diagram. The resistors R1​ and R2​ do not rotate. Then the current through the resistor R1​ is

2R1​Bωr2​

2R2​Bωr2​

2R1​R2​Bωr2​(R1​+R2​)

2(R1​+R2​)Bωr2​