Chapter 23: Q. 22 (page 654)

Two circular disks spaced $0.50 mm$ apart form a parallel-plate capacitor. Transferring $3.0 \times 10^{9}$ electrons from one disk to the other causes the electric field strength to be $2.0 \times 10^{5} N / C$ . What are the diameters of the disks?

Short Answer

Expert verified

Diameter of disk is $1.85 cm$ .

Step by step solution

Formula for area and Electric field intensity

Electric field between capacitor is $2 \times 10^{5} N / C$

Charge is $3 \times 10^{9}$ charge of electron.

$Q$ $=$ $(3 \times 10^{9})$ $\times$ $(1.6 \times 10^{- 19}) C$

Area of circle of radius $r$ is,

$A = {πr}^{2} . . . . . . . . 1$

Electric field due to parallel plate capacitor is,

$E = \frac{Q}{ϵ_{o} A} . . . . . . . . . . . . 2$

Calculation for radius of disk

Substitute equation $1$ in equation $2$ then value of $r$ is given by,

$E = \frac{Q}{ϵ_{o} {πr}^{2}}$

$r^{2} = \frac{Q}{ϵ_{O} πE}$

$r = \sqrt{\frac{Q}{ϵ_{o} πE}}$

$= \sqrt{\frac{3 \times 10^{9} \times 1.6 \times 10^{- 19} C}{π (8.85 \times 10^{- 12} C^{2} / N \cdot m^{2}) (2 \times 10^{5} N / C)}}$

$r = 9.29 \times 10^{- 3} m$

Calculation for diameter of disk

Substitute $r = 9.29 \times 10^{- 3} m$ in below formula,

$D = 2 r$

$D = 2 \times (9.29 \times 10^{- 3})$

$D = 1.85 cm$

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Two circular disks spaced $0.50 mm$ apart form a parallel-plate capacitor. Transferring $3.0 \times 10^{9}$ electrons from one disk to the other causes the electric field strength to be $2.0 \times 10^{5} N / C$ . What are the diameters of the disks?

Short Answer

Step by step solution

Formula for area and Electric field intensity

Calculation for radius of disk

Calculation for diameter of disk

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Two circular disks spaced0.50mmapart form a parallel-plate capacitor. Transferring3.0×109electrons from one disk to the other causes the electric field strength to be2.0×105N/C. What are the diameters of the disks?

Short Answer

Step by step solution

Formula for area and Electric field intensity

Calculation for radius of disk

Calculation for diameter of disk

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Radiation

Turning Points in Physics

Physics of Motion

Wave Optics

Fundamentals of Physics

Modern Physics

Study anywhere. Anytime. Across all devices.

Two circular disks spaced $0.50 mm$ apart form a parallel-plate capacitor. Transferring $3.0 \times 10^{9}$ electrons from one disk to the other causes the electric field strength to be $2.0 \times 10^{5} N / C$ . What are the diameters of the disks?