Find the force experienced by the s...
Question

# Find the force experienced by the semicircular rod charged with a charge q, placed as shown in figure. Radius of the wire is ( mathrm{R} ) and the infinitely long line of charge with linear density ( lambda ) is passing through its to the plane of wirn centre and perpendicular to the plane of wire.(A) ( frac{lambda q}{2 pi^{2} varepsilon_{0} R} )(B) ( frac{lambda q}{pi^{2} varepsilon_{0} R} )(C) ( frac{lambda q}{4 pi^{2} varepsilon_{0} R} )(D) ( frac{lambda q}{4 pi varepsilon_{0} R} )

JEE/Engineering Exams
Physics
Solution
64
4.0 (1 ratings)

( d F=E cos theta d q( ) where Eistheelectricfield
ofthechargedrod Electricfieldatthelocationofthechargedq
( i s )
( E=frac{lambda}{2 pi in R} )
( d q=frac{q}{pi R} times R d theta )
( d F=frac{lambda cos theta}{2 pi in R} frac{q}{pi R} times R d theta )
( int d F=int frac{lambda cos theta}{2 pi epsilon R} frac{q}{pi} times d theta )
( F=int_{-frac{pi}{2}}^{+frac{pi}{2}} frac{lambda cos theta}{2 pi in R} frac{q}{pi} times d theta )
( F=int_{-frac{pi}{2}}^{+frac{pi}{2}} frac{lambda cos theta}{2 pi in R} frac{q}{pi} times d theta )
( F=frac{lambda q}{2 pi^{2} in R}(sin theta)^{frac{pi}{2}}=frac{2 lambda q}{2 pi^{2} in R} )
( F=frac{lambda q}{pi^{2} in R} )
The text passage contains a physics problem that involves calculating the force experienced by a semicircular rod charged with a charge \( q \) due to an infinitely long line of charge with linear density \( \lambda \). The solution to the problem is provided, showing the step-by-step derivation of the force.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Find the force experienced by the s...
Question

# Find the force experienced by the semicircular rod charged with a charge q, placed as shown in figure. Radius of the wire is ( mathrm{R} ) and the infinitely long line of charge with linear density ( lambda ) is passing through its to the plane of wirn centre and perpendicular to the plane of wire.(A) ( frac{lambda q}{2 pi^{2} varepsilon_{0} R} )(B) ( frac{lambda q}{pi^{2} varepsilon_{0} R} )(C) ( frac{lambda q}{4 pi^{2} varepsilon_{0} R} )(D) ( frac{lambda q}{4 pi varepsilon_{0} R} )

JEE/Engineering Exams
Physics
Solution
64
4.0 (1 ratings)

( d F=E cos theta d q( ) where Eistheelectricfield
ofthechargedrod Electricfieldatthelocationofthechargedq
( i s )
( E=frac{lambda}{2 pi in R} )
( d q=frac{q}{pi R} times R d theta )
( d F=frac{lambda cos theta}{2 pi in R} frac{q}{pi R} times R d theta )
( int d F=int frac{lambda cos theta}{2 pi epsilon R} frac{q}{pi} times d theta )
( F=int_{-frac{pi}{2}}^{+frac{pi}{2}} frac{lambda cos theta}{2 pi in R} frac{q}{pi} times d theta )
( F=int_{-frac{pi}{2}}^{+frac{pi}{2}} frac{lambda cos theta}{2 pi in R} frac{q}{pi} times d theta )
( F=frac{lambda q}{2 pi^{2} in R}(sin theta)^{frac{pi}{2}}=frac{2 lambda q}{2 pi^{2} in R} )
( F=frac{lambda q}{pi^{2} in R} )
user
The text passage contains a physics problem that involves calculating the force experienced by a semicircular rod charged with a charge \( q \) due to an infinitely long line of charge with linear density \( \lambda \). The solution to the problem is provided, showing the step-by-step derivation of the force.

TYPE: SINGLE_QUESTION_WITH_ANSWER