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Two parallel wires in the plane of the paper are distance X_{0

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Two parallel wires in the plane of the paper are distance $X_{0}$ 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 $R_{1}$ . 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 $\frac{X _{0}}{X _{1}} = 3$ , and value of $\frac{R _{1}}{R _{2}}$ is ...........

Uploaded: 2023-09-02T07:47:30.000Z
Duration: 4 min

Views: 5,973 students

Updated on: Sep 2, 2023

Book:

Electricity and Magnetism (DC Pandey)

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Two parallel wires in the plane of the paper are distance

X_{0}

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

R_{1}

. 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

\frac{X _{0}}{X _{1}} = 3

, and value of

\frac{R _{1}}{R _{2}}

is ...........

6 mins ago

Discuss this question LIVE

6 mins ago

Text solutionVerified

(3)

B_{2} = \frac{μ _{0} l}{2 π x _{1}} + \frac{μ _{0} l}{2 π ( x _{0} - x _{1} )}

(when currents are in opposite directions)

B_{1} = \frac{μ _{0} I}{2 π x _{1}} - \frac{μ _{0} I}{2 π ( x _{0} - x _{1} )}

(when currents are in same direction)

Substituting x_{1} B_{1} R_{1} R_{2} = \frac{x _{0}}{3} (as \frac{x _{0}}{x _{1}} = 3) = \frac{3 μ _{0} !}{2 π x _{0}} - \frac{3 μ _{0} !}{4 π x _{0}} = \frac{3 μ _{0} I}{4 π x _{0}} = \frac{m v}{q B _{1}} and B_{2} = \frac{9 μ _{0} l}{4 π x _{0}} = \frac{m v}{q B _{2}} \Rightarrow \frac{R _{1}}{R _{2}} = \frac{B _{2}}{B _{1}} = \frac{9}{3} = 3

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Question Text	Two parallel wires in the plane of the paper are distance $X_{0}$ 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 $R_{1}$ . 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 $\frac{X _{0}}{X _{1}} = 3$ , and value of $\frac{R _{1}}{R _{2}}$ is ...........
Updated On	Sep 2, 2023
Topic	Moving Charges and Magnetism
Subject	Physics
Class	Class 12
Answer Type	Text solution:1 Video solution: 1
Upvotes	151
Avg. Video Duration	4 min

Text solutionVerified

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