Answer:
The magnitude of the magnetic field vector is 1.91T and is directed towards the east.
The steps to the solution can be found in the attachment below.
Explanation:
For the charge to remain in the the earth' gravitational field the magnetic force on the charge must be equal to the earth's gravitational force on the charge and must act opposite the direction of the earth's gravitational force.
Fm = Fg
qvBSin(theta) = mg
Where q = magnitude of charge
v = magnitude of the velocity vector = 4 x10^4 m/s
B = magnitude of the magnetic field vector
theta = the angle between the magnetic field and velocity vectors = 90°
m = mass of the charge = 0.195g
g = acceleration due to gravity =9.8m/s²
On substituting the respective values of all variables in the equation (1) above
B = 1.91T
The direction of the magnetic field vector was found by the application of the right hand rule: if the thumb is pointed in the direction of the magnetic force and the index finger is pointed in the direction of the velocity vector, the middle finger points in the direction of the magnetic field.
Below is the step by step procedure to the solution.
Answer:
The spring's maximum compression will be 2.0 cm
Explanation:
There are two energies in this problem, kinetic energy 
and elastic potential energy 
(with m the mass, v the velocity, x the compression and k the spring constant. ) so the total mechanical energy at every moment is the sum of the two energies:
Here we have a situation where the total mechanical energy of the system is conserved because there are no dissipative forces (there's no friction), so:
Note that at the initial moment where the hockey puck has not compressed the spring all the energy of the system is kinetic energy, but for a momentary stop all the energy of the system is potential elastic energy, so we have:
(1)
Due conservation of energy the equality (1) has to be maintained, so if we let k and m constant x has to increase the same as v to maintain the equality. Therefore, if we increase velocity to 2v we have to increase compression to 2x to conserve the equality. This is 2(1.0) = 2.0 cm
Answer:
The tension in the rope is 20 N
Solution:
As per the question:
Mass of the object, M = 2 kg
Density of water, 
Density of the object, 
Acceleration due to gravity, g = 
Now,
From the fig.1:
'N' represents the Bouyant force and T represents tension in the rope.
Suppose, the volume of the block be V:
V = 
(1)
Also, we know that Bouyant force is given by:
Using eqn (1):
From the fig.1:
N = Mg + T
40 = 2(10) + T
T = 40 - 20 = 20 N
Air gap means that the dielectric is air.
So <span>ε0 = </span><span>8.85 x 10^-12 [F/m].......................permitivity of free space
Lets use the equation
</span>C= ( ε0x A) / d
Where A is the area of the plate
And d the distance between the plates
d = <span>3.2-mm = 3.2 E-3 m
so ............> A = C *d /</span>ε0 = 0.20 F * 3.2 E-3 m / 8.85 x 10^-12 [F/m]
A = 7.23 E 7 [m2]
