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Long uniformly charged circular cylinder R ,has surface charge density sigma .a very long uniformly charged line charge of lambda linear density .is placed along cylindrical axxis .if electric field intensity vector outside cylinder is zero .then .what is the value of .lambda .?
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Long uniformly charged circular cylinder R ,has surface charge density...
Explanation:
When a long uniformly charged circular cylinder is given and a long uniformly charged line charge is placed along its cylindrical axis, we need to find the value of lambda such that the electric field intensity vector outside the cylinder is zero.
Electric Field Intensity Outside the Cylinder:
When we consider a point outside the cylinder, the electric field intensity is given by the equation:
E = (λ/2πε0r) + (σr/2ε0)
where λ is the linear density of the charged line, σ is the surface charge density of the cylinder, r is the distance from the axis of the cylinder, and ε0 is the permittivity of free space.
Since the electric field intensity outside the cylinder is zero, we can set the above equation to zero and solve for λ.
0 = (λ/2πε0r) + (σr/2ε0)
λ = -(2πε0σr^2)/r
λ = -2πε0σr
Conclusion:
Therefore, the value of lambda is given by -2πε0σr, where r is the distance from the axis of the cylinder. This means that the linear density of the charged line must be negative and proportional to the distance from the axis of the cylinder. This ensures that the electric field intensity outside the cylinder is zero.
When a long uniformly charged circular cylinder is given and a long uniformly charged line charge is placed along its cylindrical axis, we need to find the value of lambda such that the electric field intensity vector outside the cylinder is zero.
Electric Field Intensity Outside the Cylinder:
When we consider a point outside the cylinder, the electric field intensity is given by the equation:
E = (λ/2πε0r) + (σr/2ε0)
where λ is the linear density of the charged line, σ is the surface charge density of the cylinder, r is the distance from the axis of the cylinder, and ε0 is the permittivity of free space.
Since the electric field intensity outside the cylinder is zero, we can set the above equation to zero and solve for λ.
0 = (λ/2πε0r) + (σr/2ε0)
λ = -(2πε0σr^2)/r
λ = -2πε0σr
Conclusion:
Therefore, the value of lambda is given by -2πε0σr, where r is the distance from the axis of the cylinder. This means that the linear density of the charged line must be negative and proportional to the distance from the axis of the cylinder. This ensures that the electric field intensity outside the cylinder is zero.
Community Answer
Long uniformly charged circular cylinder R ,has surface charge density...
Is it (-2πεoRσ)
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Long uniformly charged circular cylinder R ,has surface charge density sigma .a very long uniformly charged line charge of lambda linear density .is placed along cylindrical axxis .if electric field intensity vector outside cylinder is zero .then .what is the value of .lambda .?
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Long uniformly charged circular cylinder R ,has surface charge density sigma .a very long uniformly charged line charge of lambda linear density .is placed along cylindrical axxis .if electric field intensity vector outside cylinder is zero .then .what is the value of .lambda .? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Long uniformly charged circular cylinder R ,has surface charge density sigma .a very long uniformly charged line charge of lambda linear density .is placed along cylindrical axxis .if electric field intensity vector outside cylinder is zero .then .what is the value of .lambda .? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Long uniformly charged circular cylinder R ,has surface charge density sigma .a very long uniformly charged line charge of lambda linear density .is placed along cylindrical axxis .if electric field intensity vector outside cylinder is zero .then .what is the value of .lambda .?.
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