Answer:
Magnitude of the force is 2.135N and the direction is 41.8° below negative y-axis
Explanation:
The stiff wire 50.0cm long bent at a right angle in the middle
One section lies along the z axis and the other is along the line y=2x in the xy plane

tan θ = 2
Therefore,
slope m = tan θ = y / x

Then length of each section is 25.0cm
so, length vector of the wire is

And magnetic field is B = (0.318T)i
Therefore,

![\bar F = (20.0)[(0.112m)i +(0.224m)j-(0.250m)k \times 90.318T)i]](https://tex.z-dn.net/?f=%5Cbar%20F%20%3D%20%2820.0%29%5B%280.112m%29i%20%2B%280.224m%29j-%280.250m%29k%20%5Ctimes%2090.318T%29i%5D)
![= (20.0)(i(0)+j(-0.250)(0.318T)+k[0-(0.224m)(0.318T)]\\\\=(20.0)(-0.250)(0.318)j-(20.0)(0.224)(0.318T)\\\\=-(1.59N)j-(1.425N)k](https://tex.z-dn.net/?f=%3D%20%2820.0%29%28i%280%29%2Bj%28-0.250%29%280.318T%29%2Bk%5B0-%280.224m%29%280.318T%29%5D%5C%5C%5C%5C%3D%2820.0%29%28-0.250%29%280.318%29j-%2820.0%29%280.224%29%280.318T%29%5C%5C%5C%5C%3D-%281.59N%29j-%281.425N%29k)
Magnitude of the force is

Direction is

Magnitude of the force is 2.135N and the direction is 41.8° below negative y-axis
Answer:
B_o = 1.013μT
Explanation:
To find B_o you take into account the formula for the emf:

where you used that A (area of the loop) is constant, an also the angle between the direction of B and the normal to A.
By applying the derivative you obtain:

when the emf is maximum the angle between B and the normal to A is zero, that is, cosθ = 1 or -1. Furthermore the cos function is 1 or -1. Hence:

hence, B_o = 1.013μT
Answer:
0.0133 A
Explanation:
The time at which B=1.33 T is given by
1.33 = 0.38*t^3
t = (1.33/0.38)^(1/3) = 1.52 s
Using Faraday's Law, we have
emf = - dΦ/dt = - A dB/dt = - A d/dt ( 0.380 t^3 )
Area A = pi * r² = 3.141 *(0.025 *0.025) = 0.00196 m²
emf = - A*(3*0.38)*t^2
thus, the emf at t=1.52 s is
emf = - 0.00196*(3*0.38)*(1.52)^2 = -0.0052 V
if the resistance is 0.390 ohms, then the current is given by
I = V/R = 0.0052/0.390 = 0.0133 A
Explanation:
It is given that,
Mass of bumper car, m₁ = 202 kg
Initial speed of the bumper car, u₁ = 8.5 m/s
Mass of the other car, m₂ = 355 kg
Initial velocity of the other car is 0 as it at rest, u₂ = 0
Final velocity of the other car after collision, v₂ = 5.8 m/s
Let p₁ is momentum of of 202 kg car, p₁ = m₁v₁
Using the conservation of linear momentum as :


p₁ = m₁v₁ = -342 kg-m/s
So, the momentum of the 202 kg car afterwards is 342 kg-m/s. Hence, this is the required solution.