phy E&M electrostatic (urgent)

2011-04-30 3:01 am

1. An insolated metal sphere has a total charge of 1.2 x 10 ^ -8 C. The insulation of air breaks down when, the field strength is 3 x 10^6 V/m. What is the smallest possible radius of the sphere? (Ans: 6 x 10-3m)
I want the steps

2.A charged ball X is suspended by a string. When a uniform electric field E is applied horizontally, the ball is displaced a horizontal distance a such that the string makes an angle x with the vertical.
Show that E is proportional to sin x for small values of x only.

3. A potential difference V is applied between 2 large parallel plates, distance s apart. An electron of mass m and charge -e starts from rest at the negative plate and travels across the gap to the positive plate. Show that the time takes is sqrt((2ms^2) / eV)

4. 'The force exerted on a charge of 1 coulomb in an electrostatic field of 1 volt/metre is 1 newton.' Why is the correct?

5.A charged particle is accelerated across the gap between 2 parallel metal plated maintained at a certain potential difference in a vacuum. Assuming there is no gravitational force, why the energy acquired by the charged particle in crossing the gap does not depend on the width of the gap? according to E = V/d, d should affects E. Please explain.

6. What is meant by 'the charge density on the surface of a metal sphere'?

thanks

回答 (1)

天同

2011-04-30 4:38 am

✔ 最佳答案

1. electric field at sphere surface = k(1.2x10^-8)/R^2
where R is the sphere radius and k is a constant with value of 9x10^9 F/m
hence, for breakdown to occur, k(1.2x10^-8)/R^2 = 3x10^6solve for R gives R = 6x10^-3 m
2. Let T be the tension in the string and m be the mass of the ballwe have, T.sin(x) = qE, where q is the charge on the balland T.cos(x) = mg, where g is the acceleration due to gravityDividing, T.sin(x)/T.cos(x) = qE/mgi.e. E = (mg/q.cos(x)).sin(x)
For small value of x, cos(x) ~ 1,
hence, .E = (mg/q).sin(x), or E is proportional to sin(x)

3. Acceleration of electron = force/mass = [e(V/s)]/mUse equation of motion: s = ut + (1/2)at^2hence, s = (1/2)(eV/sm)t^2i.e. t^2 = 2s^2m/eV

4. From the definition of electric field intensity E, which is the force per unit charge.
i.e. E = force/charge
i.e. force = charge x E, = 1 x 1 N = 1 N
5. SImilar to Q3, the acceleration of the particle = qV/dm
where q and m are the charge and mass of the particle
use equation of motion: v^2 = u^2 + 2as
hence, v^2 = 2(qV/dm)d
i.e. v^2 = 2qV/m
Kinetic energy acquired by the particle
= (1/2)mv^2 = (m/2).(2qV/m) = qV
which is independent of d

6. surface charge density is the charge (in coulomb) per unit area (in metre square).

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