Two parallel wires in the plane of the paper are distance X0 apart. A point charge is moving with speed u between the wires in the same plane at a distance X 1 from one of the wires. When the wires carry current of magnitude I in the same direction, the radius of curvature of the path of the point charge is R1. In contrast, if the currents I in the two wires have directions opposite to each other, the radius of curvature of the path is R 2 . If ( X 0/ X 1)=3, the value of ( R 1/ R 2) is

Question

Two parallel wires in the plane of the paper are distance X0 apart. A point charge is moving with speed u between the wires in the same plane at a distance X 1 from one of the wires. When the wires carry current of magnitude I in the same direction, the radius of curvature of the path of the point charge is R1. In contrast, if the currents I in the two wires have directions opposite to each other, the radius of curvature of the path is R 2 . If ( X 0/ X 1)=3, the value of ( R 1/ R 2) is (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/eaaf196d89b58ee5ac506f77c1bb4d7a-.png" /> B 1=(1/2)((μ0/2 π))((3 I / x 0)) R 1=( mv / q B 1) R 2=( mv / qB 2) ⇒ ( R 1/ R 2)=( B 2/ B 1)=(1 / 3/1 / 9)=3

B1​=21​(2πμ0​​)(x0​3I​) R1​=qB1​mv​ R2​=qB2​mv​ ⇒R2​R1​​=B1​B2​​=1/91/3​=3

$B_{1} = \frac{1}{2} (\frac{μ _{0}}{2 π}) (\frac{3 I}{x _{0}})$
$R_{1} = \frac{m v}{q B _{1}}$
$R_{2} = \frac{m v}{q B _{2}}$
$\Rightarrow \frac{R _{1}}{R _{2}} = \frac{B _{2}}{B _{1}} = \frac{1/3}{1/9} = 3$