Answe
a) Q = 0.820 10⁻⁹ C
, b) Q = -3.52 10⁻⁹ C
Explanation:
The electric field is given by the formula
E = k q / r²
where E is a vector quantity, so it must be added as a vector
E_total = E₁ + E₂
let's look for the two electric fields
E₁ = k q₁ / r₁²
E₁ = 9 10⁹ 5.4 10⁻⁹ / 1.25²
E₁ = 31.10 N / C
E2 = k Q / r₂²
E2 = 9 10⁹ Q / 0.625²
E2 = 23.04 10⁹ Q N / C (1)
now we can solve the two cases presented
a) The total field is
E_total = 50.0 N / C towards + x
since the test charge is positive the electric field E1 points to the right in the direction of the + x axis, so the equation is
E_total = E1 + E₂
E₂ = E_toal - E₁
E₂ = 50.0 -31.10
E2 = 18.9 N /C
With the value of the electric field we can calculate the charge (Q) using equation 1
E₂ = 23.04 10⁹ Q
Q = E₂ / 23.04 10⁹
Q = 18.9 / 23.04 10⁹
Q = 0.820 10⁻⁹ C
the charge on Q is positive
b) E_total = -50.0 N / C
E_total = E₁ + E₂
E₂ = E_total - E₁
E2 = -50.0 - 31.10
E2 = -81.10 N /C
we calculate the charge
Q = E2 / 23.04 10⁹
Q = -81.1 / 23.04 10⁹
Q = -3.52 10⁻⁹ C
for this case the charge is negative
Answer:
1.) answer B
2.) answer D
3.) answer A
Explanation:
In all of these problems, it is essential to draw pictures in order to understand which trigonometric function to use according to the angle that the vector in question forms with the component requested. For all of them try to picture a right angle triangle with the vector as the hypotenuse, and the components as the triangle's shorter sides. Please refer to the three pictures attached as image for this answer a,d notice that the vector quantity known for all cases is represented in red, and the component to find is represented in green.
Problem 1) : the vector velocity makes an angle of 24 degrees with the edge of the table. So picture that vector as the hypotenuse of a right angle triangle for which you know the value: 1.8 m/s
So in this case, where you know the angle, the hypotenuse, and need to find the adjacent side to the angle, you use the cosine function as follows:
requested component 
which we round to 1.6 to match answer C).
For problem 2.) wee need to find the component opposite to the given angle in the triangle for which we also know the hypotenuse. So we use the sine function as follows:
requested component 
which we round to 135.9 m to match answer D).
For problem 3.) we need to find the horizontal component to the acceleration which corresponds to the adjacent side to the known angle, so we use the cosine function as follows:
requested component 
which we round tp 7.7 to match answer A).
The north arrow of the compasses will all point to the south since opposite poles attract. I have put an example picture below.
For the horse shoe magnet the magnetic field line will also go from north to south. I have put a picture of this below
The resistance is 4 times the resistance of the first wire. the formula is R = p*l/A with p being resistivity, l length and A area. So if you double length and half area, which botv result in more resistance, you get p*2/0.5 or 4 (p can be abandoned because it is the same. We take standard length and area as 1)