Specific Charge Ratio Experiments

Question 1

What does ‘specific charge’ mean in physics?

Answer 1

Specific charge is the charge-to-mass ratio of a particle, calculated using:

( \frac{e}{m} )

Question 2

What is a fine beam tube and how is it used to measure specific charge?

Answer 2

It contains low-pressure gas and a uniform magnetic field. Electrons are accelerated and move in a circular path due to the magnetic force acting as centripetal force.

Question 3

How does the electron path become visible in a fine beam tube?

Answer 3

Electrons excite gas atoms, which de-excite and emit photons, revealing the circular path of the beam.

Question 4

What equations are used in the fine beam tube method?

Answer 4

Magnetic force provides centripetal force:

( \frac{mv^2}{r} = Bev )

From energy conservation:

( \frac{1}{2} mv^2 = eV \Rightarrow v = \sqrt{\frac{2eV}{m}} )

Question 5

Derive the formula for specific charge using fine beam tube values.

Answer 5

( \frac{e}{m} = \frac{2V}{B^2 r^2} )

Where:
- ( V ) is accelerating voltage
- ( B ) is magnetic field strength
- ( r ) is radius of the electron path

Question 6

What are crossed fields in Thomson’s method?

Answer 6

Magnetic and electric fields that are perpendicular to each other and to the path of the electron beam.

Question 7

What condition is used to find velocity in crossed fields?

Answer 7

The electric and magnetic forces are balanced (no deflection):

( Bev = e \frac{V}{d} \Rightarrow v = \frac{Bd}{V} )

Question 8

What energy equation is used for the accelerated electrons in this setup?

Answer 8

( \frac{1}{2} mv^2 = eV_a \Rightarrow v^2 = \frac{2eV_a}{m} )

Question 9

Derive the equation for specific charge using Thomson’s crossed fields method.

Answer 9

( \frac{e}{m} = \frac{V^2}{2B^2 d^2 V_a} )

Where:
- ( V ) = Electric field voltage
- ( d ) = Plate separation
- ( B ) = Magnetic field strength
- ( V_a ) = Accelerating voltage

Question 10

Why was Thomson’s measurement of specific charge important?

Answer 10

It showed the specific charge of the electron was the same for all gases, proving electrons are universal components of atoms.

Question 11

What atomic model did Thomson propose based on his findings?

Answer 11

The plum pudding model – electrons embedded in a sphere of positive charge.

Question 12

What is the approximate specific charge of an electron?

Answer 12

1.76 × 10^11 C/kg

Question 13

How does the specific charge of a proton compare to that of an electron?

Answer 13

Proton: 9.58 × 10^7 C/kg

The electron’s specific charge is about 1800 times larger than a proton’s.