Awire loop with 70 turns is formed into a square with sides of length . the loop is in the presence of a 1.20 t uniform magnetic field ⃗ that points in the negative y direction. the plane of the loop is tilted off the x-axis by theta=15∘ . if =1.50 a of current flows through the loop and the loop experiences a torque of magnitude 0.0294 n⋅m , what are the lengths of the sides of the square loop, in centimeters?

l= 3.002 cm

Explanation:

Given that

n= 70 turns

B= 1.2 T

θ= 15°

I= 1.5 A

τ = 0.0294 N⋅m

Lets take length of sides is l.

We know that

τ  = n I A B sin θ

Area of square ,A= l²

Now by putting the value

τ  = n I A B sin θ

0.0294  = 70 x  1.5 x  l² x  1.2 x  sin 15°

l² = 0.000901 m²

l² = 9.01 cm²

l= 3.002 cm

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.