Answer:
The movement of polar bears help figure out the impact of global warming in the arctic. Since polar bears travel over the frozen ocean they are able to determine the rate it melts as the bears retreat inland. The worse global warming become the quicker it becomes hotter in the arctic which is bad by the way.
Explanation:
Answer:
Same direction to produce maximum magnitude and opposite direction to produce minimum magnitude
Explanation:
Let a be the angle between vectors A and B. Generally when we add A to B, we can split A into 2 sub vectors, 1 parallel to B and the other perpendicular to B.
Also let A and B be the magnitude of vector A and B, respectively.
We have the parallel component after addition be
Acos(a) + B
And the perpendicular component after addition be
Asin(a)
The magnitude of the resulting vector would be
![\sqrt{(Acos(a) + B)^2 + (Asin(a))^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28Acos%28a%29%20%2B%20B%29%5E2%20%2B%20%28Asin%28a%29%29%5E2%7D)
![= \sqrt{A^2cos^2a + B^2 + 2ABcos(a) + A^2sin^2a}](https://tex.z-dn.net/?f=%20%3D%20%5Csqrt%7BA%5E2cos%5E2a%20%2B%20B%5E2%20%2B%202ABcos%28a%29%20%2B%20A%5E2sin%5E2a%7D)
![= \sqrt{A^2(cos^2a + sin^2a) + B^2 + 2ABcos(a)}](https://tex.z-dn.net/?f=%20%3D%20%5Csqrt%7BA%5E2%28cos%5E2a%20%2B%20sin%5E2a%29%20%2B%20B%5E2%20%2B%202ABcos%28a%29%7D)
![= \sqrt{A^2 + B^2 + 2ABcos(a)}](https://tex.z-dn.net/?f=%20%3D%20%5Csqrt%7BA%5E2%20%2B%20B%5E2%20%2B%202ABcos%28a%29%7D)
As A and B are fixed, the equation above is maximum when cos(a) = 1, meaning a = 0 degree and vector A and B are in the same direction, and minimum with cos(a) = -1, meaning a = 180 degree and vector A and B are in opposite direction.
Answer:
Current is calculated as the amount of charge that pass a point on a circuit per time.
Explanation:
Electric current is defined as the amount of charge that passes a point on a circuit per unit time. The mathematical definition of electric current is given by :
![I=\dfrac{q}{t}](https://tex.z-dn.net/?f=I%3D%5Cdfrac%7Bq%7D%7Bt%7D)
Where
q is a charge (Coulomb)
t is time (in seconds)
The SI unit of electric current is A. It is equivalent to C/s. So, the correct option is (A).
Answer:
Attached below
Explanation:
The plot showing the potential as a function of distance from the center of the sphere is attached below
note : The Potential inside the sphere will remain constant as potential remains constant on surface and it start to decrease as 1/r
Answer:
The current in the coil is 60 Ampere.
Explanation:
Given:
Number of turns in the coil is N = 25
Dimension of the coil = 15cm X 12cm
magnitude of magnetic field = 0.20T
angle in the xy plane is θ = 0 degree
torque τ = 5.4 N-m
To find:
current in the coil is i = ?
Solution:
The torque acting on the coil is given by
=> ![\tau = NiAB cos\theta](https://tex.z-dn.net/?f=%5Ctau%20%3D%20NiAB%20cos%5Ctheta)
Converting cm to m
12 cm = 0.12 m
15 cm = 0.15 m
The area of the coil is
A = 0.12 X 0.15
A = ![0.018 m^2](https://tex.z-dn.net/?f=0.018%20m%5E2)
Substituting the values
=>![5.4 = 25\times i \times 0.018 \times 0.20 \times cos\theta](https://tex.z-dn.net/?f=5.4%20%3D%2025%5Ctimes%20i%20%5Ctimes%200.018%20%5Ctimes%200.20%20%5Ctimes%20cos%5Ctheta)
=>![5.4 = 25\times i \times 0.018 \times 0.20 \times cos(0)](https://tex.z-dn.net/?f=5.4%20%3D%2025%5Ctimes%20i%20%5Ctimes%200.018%20%5Ctimes%200.20%20%5Ctimes%20cos%280%29)
=>![5.4 = 25\times i \times 0.018 \times 0.20 \times 1](https://tex.z-dn.net/?f=5.4%20%3D%2025%5Ctimes%20i%20%5Ctimes%200.018%20%5Ctimes%200.20%20%5Ctimes%201)
=>![5.4 = 25\times i \times 0.018 \times 0.20 \times 1](https://tex.z-dn.net/?f=5.4%20%3D%2025%5Ctimes%20i%20%5Ctimes%200.018%20%5Ctimes%200.20%20%5Ctimes%201)
=>![5.4 = 0.09\times i](https://tex.z-dn.net/?f=5.4%20%3D%200.09%5Ctimes%20i)
=>![i = \frac{5.4}{0.09}](https://tex.z-dn.net/?f=i%20%3D%20%5Cfrac%7B5.4%7D%7B0.09%7D)
=> i = 60 A