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Gauss Theorem – Electrostatics

DIVYA asked:

“WHAT IS THE  MAGNITUDE OF ELECTRIC  FIELD IN THE  GAUSSIAN SURFACE OF  A CUBE,AT ITS FACE ,AT ITS CENTRE, AT ITS CORNERS OR AT ANY OTHER POINT INSIDE THE CUBE. ALSO TELL ME THE THE WAY TO KNOW IT.”

Ans:

According to Gauss Theorem, the total electric flux through a closed surface,\oint_S \mathbf{E} \cdot \mathrm{d}\mathbf{A}  = \frac{Q}{\varepsilon_0},

The Gaussian surface is an imaginary surface. So, for calculating the electric field at a point using Gauss theorem, we have to imagine a Gaussian surface symmetric with the given charge distribution.

I have assumed that there is a point charge Q at the centre of the cube.

At its face (at a point on the face on the line radially outwards from the point charge at the centre of the cube and perpendicular to the face)

The distance is equal to half the length of side of the cube (Say L).

Therefore the electric field,image  

 

On the corner,

Calculate the distance from the centre of the cube to its corner and replace (L/2) in the above equation with that distance.

Time Period of a Simple Pendulum in Space

Mary Beth asked:

“if you set up a pendulum aboard an orbiting space vehicle, would the period be less than, the same as, or greater than it would be in our lab? explain.”

Ans:

In a space vehicle orbiting around the earth, the apparent weight is zero as the entire gravitational pull is being utilized in providing the centripetal force required for revolving. This is called weightlessness in space.

i.e; in effect, the acceleration due to gravity is zero which make the time period of the satellite infinity. The pendulum will not oscillate at all.

__________________________________________________________

Tailpiece:

However, in manned space vehicles, there is an option to simulate gravity by making the system rotate at a particular rate so as to make the inhabitants feel as if there is weight and gravity.

Pendulum on Mount Everest !

Michelle Guzman Asked:

If you set a pendulum atop Mt. Everest, would the period be less than, greater than or equal to the period you would get in the lab?  Explain.

Ans:

As you know, the acceleration due to gravity decreases as we go upwards from surface of earth.

The time period of a simple pendulum is given by

Where l is the length of the pendulum, and g is the acceleration due to gravity.

From the equation, we can conclude that, the Time period of the pendulum increases (i.e. it goes slower)  if the pendulum is set up on top of Mount Everest.

For Creative and Critical Thinkers

Here we have not considered the change in temperature between the laboratory conditions and the temperature on top of Mount Everest which is very low. A decrease in temperature would decrease the length of the pendulum (Unless it is made up of such a substance which does not change its length with change in  temperature) and will also decrease the time period of the pendulum, making it move faster.

My first answer is correct only if the laboratory conditions are the same as on top of Mt. Everest or vice versa, except for the difference in altitude (height)

Ask Physics

A question from Kinetic energy

Atul asked:

A lorry and a car moving with the same KE are brought to rest having same retarding force .which one of them should come at rest at shorter distance.

 

Ans:

According to Work Kinetic Energy theorem

Both should stop travelling the same distance

(This was a quick answer without a deep thought. If the readers have a diffrent opinion, please comment)

Numericals from Kinematics

Posted By – Abdul Hameed

  1. During the first 18 minutes of a 1.0-hour trip, a car has an average speed of 11 m/s. What must the average speed of the car be during the last 42 minutes of the trip be if the car is to have an average speed of 21 m/s for the entire trip?
  2. An elevator is moving upward with a speed of 11 m/s. Three seconds later, the elevator is still moving upward, but its speed has been reduced to 5.0 m/s. What is the average acceleration of the elevator during the 3.0 s interval?
  3. A turtle takes 3.5 minutes to walk 18 m toward the south along a deserted highway. A truck driver stops and picks up the turtle. The driver takes the turtle to a town 1.1 km to the north with an average speed of 12 m/s. What is the magnitude of the average velocity of the turtle for its entire journey?

 

VISITORS CAN TRY TO ANSWER AS COMMENTS BY THE TIME MASTER ANSWERS THE QUESTIONS

A question from photoelectric effect

Jyothir Asked:

In photoelectric effect, what happens to the photon after it collides elastically with the electron ?

 

Ans:

The photon is completely absorbed by one electron, the energy of the electron provides the work function which is equal to the binding energy of the electron and the balance energy appears as the electrons Kinetic energy.

As Einstein’s Photo electric equation suggests

KE = h (v-vo)

A Problem from Specific Heat of Gases

Priyanshi Gaur posted”:

“A sample of air weighing 1.18g occupies 1000 cubic cm when kept at 300 K at 1000000 Pa.When 2 cal of heat is added to it at constant volume, its temperature increases by 1 degree celcius.Calculate the amount of heat needed to increase the temperature of air by 1 degree celcius at constant pressure if the mechanical equivalent of heat is 4.2*10000000 erg/cal.”

Hints:

Remember that

Cp/Cv = γ

Cp-Cv=R

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