Newton's law of gravity and Coulomb's law are both inverse-square laws. Consequently, there should be a "Gauss's law for gravity." The electric field was defined as E = Fon q/q, and we used this to find the electric field of a point charge. Using analogous reasoning, what is the gravitational field g→ of a point mass? Write your answer using the unit vector r^, but be careful with signs; the gravitational force between two "like masses" is attractive, not repulsive. Express your answer in terms of the variables M, r, unit vector r^, and the gravitational constant G. Use the 'unit vector' button to denote unit vectors in your answer.   A spherical planet is discovered with mass M, radius R, and a mass density that varies with radius as ρ=ρ0(1−r/2R), where ρ0 is the density at the center. Determine ρ0 in terms of M and R.     Gauss's law for gravity: integral ∮g →⋅ dA =−4πGMin Find an expression for the gravitational field strength inside the planet at distance r < R.

Can someone please do this task step by step.Find the electric field (magnitude and direction) a distance z above the midpoint between twoequal charges q, a distance d apart (Fig. 6).

Consider the figure below. qa Oq 9b O qd O qc (a) Using the symmetry of the arrangement, determine the direction of the electric field at the center of the square in the figure, given that q₂ = qb= -9.50 μC and q = = +9.50 μC. 8✔ toward the top of the page. (b) Calculate the magnitude of the electric field (in N/C) at the location of q, given that the square is 2.50 cm on a side. 77.7e6 X N/C ULE

Please help me in this

In the question above, charge q 2 is 2x10 -9C and charge q 1 has mass 0.23g.  The separation r is 2.5cm, and the angle θ is 15.9 degrees.  Find q 1(magnitude and sign, you don't need to enter a + for positive answers but you will need to enter a - if negative).  Note: the answer for this question is very small and using scientific notation will help.  This system uses E in place of x10 so for example to enter 3x10 -24 type 3E-24 in the answer box.

Now, you try this one. Compute the electric field experienced by a test charge q =+0.80µC from a source =+0.15µC in a vacuum when the test charge is places 0.20 m away from the other charge.

A right triangle ABC with the right triangle at vertex B. The charges at A, at B, and at C, are known to be 5 mC, 4 mC, and 7 mC, respectively. Given that the side AB is equal to 1, in meters, and AC is thrice AB, determine the magnitudes of the force and of the electric field at C.

A coaxial cylinder of length L = 5 m consists of two cylindrical shells of radii a = 15 cm and b = 20 cm, respectively (see figure). The charge of the inner cylinder shell is Q = + 17.7 μC while the outer shell charge is Q = -17.7 μC. Find the electric field strength at: rc = 10 cm, rd = 18 cm, and re = 25 cm! Please write your answer neatly and readable as well :)

A gold nucleus you emanates electric field, holding all its electrons in place. How strong is the electric field experienced by a single electron from its outermost orbital, located at 136 PM? How fast is it moving on its circular orbit, assuming it has a hypothetical plane orbit? How much kenetic energy is gained by the electron? Give full solution and illustrate the problem.

Imagine you have four identical charge q, placed on the corners of a square. If q = 14.77 uC, then the side of the square is s = 13.04 cm, calculate the energy needed to bring these charges from infinity to their current configuration. NOTE: Final answer in THREE decimal places. Then, state the SI unit of the variable being sought off. Add your answer