Answer:
The inductance of solenoid A is twice that of solenoid B
Explanation:
The inductance of a solenoid L is given by
L = μ₀n²Al where n = turns density, A = cross-sectional area of solenoid and l = length of solenoid.
Given that d₁ = 2d₂ and l₂ = 2l₁ and d₁ and d₂ are diameters of solenoids A and B respectively. Also, l₁ and l₂ are lengths of solenoids A and B respectively.
Since we have a cylindrical solenoid, the cross-section is a circle. So, A = πd²/4.
Let L₁ and L₂ be the inductances of solenoids A and B respectively.
So L₁ = μ₀n²A₁l₁ = μ₀n²πd₁²l₁/4
L₂ = μ₀n²A₂l₂ = μ₀n²πd₂²l₂/4
Since d₁ = 2d₂ and l₂ = 2l₁, sub
L₁/L₂ = μ₀n²πd₁²l₁/4 ÷ μ₀n²πd₂²l₂/4 = d₁²/d₂² × l₁/l₂ = (2d₂)²/d₂² × l₁/2l₁ = 4d₂²/d₂² × l₁/2l₁ = 4 × 1/2 = 2
L₁/L₂ = 2
L₁ = 2L₂
So, the inductance of solenoid A is twice that of solenoid B
Answer:
Part a)

Part b)

Explanation:
Part a)
As we know that the magnetic force on the current carrying wire is given as

so we have


so we have

Part b)
Now magnetic field is changed to 0.55 T
so we will have


The speed does the block move after it is hit by the bullet that remains stuck inside the block will be 23.7 m/sec and it takes 12.07 seconds to stop.
<h3>What is the law of conservation of momentum?</h3>
According to the law of conservation of momentum, the momentum of the body before the collision is always equal to the momentum of the body after the collision.
Apply the law of conservation of momentum principle;
m₁v₁+m₂v₂cosΘ =(m₁+m₂)V
3 kg × 12 m/s + 0,1 kg × 400 m/s cos 20° = (3+0.1)V
36 + 40 cos 20° = 3.1 V
V=23.7 m/sec
The time it takes to stop when the friction coefficient between the block and the surface is 0.2 is found as;
V = u +at
V = 0+ μgt
23..7=0.2× 9.81 ×t
t=12.07 sec
Hence, it takes 12.07 seconds to stop.
To learn more about the law of conservation of momentum refer;
brainly.com/question/1113396
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