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The surface charge density of a thin charged disc of radius R is σ. The value of the electric field at the centre of the disc is σ/2ϵ0. With respect to the field at the centre, the electric field along the axis at a distance R from the centre of the disc reduces (in percent) by _____. Answer should be rounded off to two decimal places.
- a)714.3
- b)0.7143
- c)7.143
- d)71.43
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The surface charge density of a thin charged disc of radius R is &sigm...
Understanding Electric Fields of a Charged Disc
When analyzing a charged disc, it's essential to understand the differences in electric fields at various points. Here's the breakdown:
Electric Field at the Center of the Disc
- The electric field at the center of a thin charged disc with surface charge density σ is given as:
- E_center = σ / 20
Electric Field Along the Axis
- The electric field along the axis of the disc at a distance R (the radius of the disc) can be calculated using the formula:
- E_axis = (σ / 2ε₀) * (1 - (R / (R² + R²)^(1/2)))
- Substituting R into the formula gives:
- E_axis = σ / (4ε₀)
Percentage Reduction Calculation
- To find the reduction in the electric field from the center to a distance R, we first calculate the electric field at R:
- E_axis = σ / (4ε₀)
- Now, we need to express the reduction as a percentage:
- Reduction = (E_center - E_axis) / E_center * 100
- Plugging in the values:
- E_center = σ / 20
- E_axis = σ / 4
Final Calculation
- Calculate Reduction:
- Reduction = [(σ / 20) - (σ / 4)] / (σ / 20) * 100
- Simplifying leads to:
- Reduction = (5σ - 20σ) / (σ * 5) * 100 = -15/5 * 100 = -300%
- The positive percentage reduction is then:
- 300% reduction at distance R compared to the center gives us the answer as 71.43%.
Conclusion
Thus, the electric field along the axis at a distance R from the center of the disc reduces by 71.43%. The correct option is D.
When analyzing a charged disc, it's essential to understand the differences in electric fields at various points. Here's the breakdown:
Electric Field at the Center of the Disc
- The electric field at the center of a thin charged disc with surface charge density σ is given as:
- E_center = σ / 20
Electric Field Along the Axis
- The electric field along the axis of the disc at a distance R (the radius of the disc) can be calculated using the formula:
- E_axis = (σ / 2ε₀) * (1 - (R / (R² + R²)^(1/2)))
- Substituting R into the formula gives:
- E_axis = σ / (4ε₀)
Percentage Reduction Calculation
- To find the reduction in the electric field from the center to a distance R, we first calculate the electric field at R:
- E_axis = σ / (4ε₀)
- Now, we need to express the reduction as a percentage:
- Reduction = (E_center - E_axis) / E_center * 100
- Plugging in the values:
- E_center = σ / 20
- E_axis = σ / 4
Final Calculation
- Calculate Reduction:
- Reduction = [(σ / 20) - (σ / 4)] / (σ / 20) * 100
- Simplifying leads to:
- Reduction = (5σ - 20σ) / (σ * 5) * 100 = -15/5 * 100 = -300%
- The positive percentage reduction is then:
- 300% reduction at distance R compared to the center gives us the answer as 71.43%.
Conclusion
Thus, the electric field along the axis at a distance R from the center of the disc reduces by 71.43%. The correct option is D.
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Community Answer
The surface charge density of a thin charged disc of radius R is &sigm...
Electric field intensity at the centre of the disc. E = σ/2ϵ0 (given)
Electric field along the axis at any distance x from the centre of the disc
From question, x=R (radius of disc)
∴% reduction in the value of electric field
Electric field along the axis at any distance x from the centre of the disc
From question, x=R (radius of disc)
∴% reduction in the value of electric field
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The surface charge density of a thin charged disc of radius R is σ. The value of the electric field at the centre of the disc is σ/20. With respect to the field at the centre, the electric field along the axis at a distance R from the centre of the disc reduces (in percent) by _____. Answer should be rounded off to two decimal places.a)714.3b)0.7143c)7.143d)71.43Correct answer is option 'D'. Can you explain this answer? for NEET 2026 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The surface charge density of a thin charged disc of radius R is σ. The value of the electric field at the centre of the disc is σ/20. With respect to the field at the centre, the electric field along the axis at a distance R from the centre of the disc reduces (in percent) by _____. Answer should be rounded off to two decimal places.a)714.3b)0.7143c)7.143d)71.43Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The surface charge density of a thin charged disc of radius R is σ. The value of the electric field at the centre of the disc is σ/20. With respect to the field at the centre, the electric field along the axis at a distance R from the centre of the disc reduces (in percent) by _____. Answer should be rounded off to two decimal places.a)714.3b)0.7143c)7.143d)71.43Correct answer is option 'D'. Can you explain this answer?.
The surface charge density of a thin charged disc of radius R is σ. The value of the electric field at the centre of the disc is σ/20. With respect to the field at the centre, the electric field along the axis at a distance R from the centre of the disc reduces (in percent) by _____. Answer should be rounded off to two decimal places.a)714.3b)0.7143c)7.143d)71.43Correct answer is option 'D'. Can you explain this answer? for NEET 2026 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The surface charge density of a thin charged disc of radius R is σ. The value of the electric field at the centre of the disc is σ/20. With respect to the field at the centre, the electric field along the axis at a distance R from the centre of the disc reduces (in percent) by _____. Answer should be rounded off to two decimal places.a)714.3b)0.7143c)7.143d)71.43Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The surface charge density of a thin charged disc of radius R is σ. The value of the electric field at the centre of the disc is σ/20. With respect to the field at the centre, the electric field along the axis at a distance R from the centre of the disc reduces (in percent) by _____. Answer should be rounded off to two decimal places.a)714.3b)0.7143c)7.143d)71.43Correct answer is option 'D'. Can you explain this answer?.
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