Question

1 ) Calculate the energy radiated in one minute by a black body of surface area 200cm^2 at 127°C.

2) Obtain equation of Lorentz force law. ​

Answer 1

Question:

Calculate the energy radiated in one minute by a black body of surface area 200 cm² at 127° C

Answer:

Energy = 1744.64 J

Explanation:

Given:

• Area = 200 cm² = 0.02 m
• Time = 1 min = 60 s
• Temperature = 127°C = 400.15 K

To Find:

• The energy radiated by the black body

Solution:

The energy radiated by a black body is given as,

$\boxed{\tt E=\sigma\:AT^4t}$

where E = energy

σ = Stefan-Boltzmann constant = 5.6703 × 10⁻⁸ W/m² K⁴

A = area

T = temperature

t = time

Substitute the data,

$\sf E = 5.6703\times 10^{-8}\times 0.02\times (400.15)^4\times 60$

$\sf \implies 5.6703\times 10^{-8}\times 1.2\times 2.564\times 10^{10}$

$\sf \implies 1744.64 J$

Hence energy radiated by the black body is 1744.64 J.

Question:

Obtain equation of Lorentz force law

Answer:

Lorentz forces are forces on charged particles due to electric and magnetic fields.

The force acting on a charged particle due to electric field is given by,

$\vec{ F_e} =q.\vec{ E}$

where E is the electric field and q is the charge.

Now the force acting on a charged particle due to magnetic field is given by,

$\vec{ F_b} =q\times\vec{V} \vec{B}$

where B is the magnetic field and V is the velocity of charged particle

Hence Lorentz force is given by,

$F_l=F_e+F_b$

$\vec{ F_l} =q.\vec{ E}+q\times \vec{V}\vec{B}$

$\boxed{\vec{ F_l} =q(\vec{ E}+\vec{V}\times\vec{B})}$

Answer 2

Given:

Surface area of the black body = 200 cm²

Temperature of the black body = 127°C

To find:

The energy radiated from the black body in one minute.

Solution:

From the Steffan Bolzmann law:

Power dissipated by black body P = AξσT⁴

Since it is a black body ξ = 1

Temperature T = 273+ 127 = 400 K

Also σ = 5.67*10⁻⁸ J/m²sK⁴

Therefore P = 200*10⁻⁴ * 1 * 5.67*10⁻⁸ * 400⁴ ≈ 29 J/s

We know that Energy = power×time

Energy = 29 J/s * 60 s = 1740 J

Therefore the energy radiated is one minute will be 1740 J.