2-47. Consider a particle moving in the region x> 0 under the influence of the potential U(x) = Uo a where U, = 1 J and a = 2 m. Plot the potential, find the equilibrium points, and determine whether they are maxima or minima. %3D
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A: A) In case of conservative force, we know that force is the negative gradient of potential energy.…
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A: Work done is given by W=∫F.dl dl=dxi^+dyj^ If a force is conservative dFxdy=dFydx
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Q: Suppose we let the radius approach zero. What would happen to the self-potential energy?
A: As we know
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Q: A conducting sphere of radius 'a' has a constant electric potential at its surface equal to V(a,0) =…
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Q: The charge density on a disk of radius R = 11.8 cm is given by o = ar, with a = 1.36 µC/m³ and r…
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Q: Let F(x, y) = 2xy³i+ (1+3x²y?)j. (a) Demonstrate that F is conservative. (b) Find the potential…
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Q: 12 TO The potential energy of two atoms separated by a distance r may be written: U(r) = 4U₁ 4.…
A: Given information: Potential energy of two atoms Ur=4U0r0r12-r0r6. Constant r0=3.3 nm. Constant…
Q: A sphere of radius a has potential (sin 2θ)( cos ϕ) on its surface. Find the potential at all points…
A: To find the potential at points outside the sphere, we can use the concept of multipole expansion.…
Q: The charge density on a disk of radius R = 12.6 cm is given by d = ar, with a = 1.34 µC/m³ and r…
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Q: The charge density on a disk of radius R = 12.2 cm is given by a=ar, with a = 1.34 μC/m3 and r…
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Q: The charge density on a disk of radius R= 13.0 cm is given by car, with a = 1.44 μC/m³ and r…
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Q: (0, 0,0) and the 5. The point o is the origin of the coordinate system, o = coordinates of b are b =…
A: (a) Given: The electric potential at point o is 0. The electric potential at point b is -∫obE→·dr→.…
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Q: F(r)=nrn-²r where, as usual, r = = x + y + z2 and r = x² + y² + z² and n is an integer.
A: For a force is conservative, its curl must be zero. That is, ∇×F→=0 where the operator ∇ is defined…
Q: Consider the gravitational force field F with G = m = M = 1 in 3D with the potential function being…
A: Given that:F(x,y,z)=1(x2+y2+z2)3(-x,-y,-z)This can be rewritten as:F(x,y,z)=1r3(-r→) since…
Q: The figure shows a potential well for a particle that can move along an x axis. Four regions of the…
A: Required : The order of force
Q: Q3) Find the potential u(r, 9) inside a ring 1 <r < 2 if the potential on the inner boundary r = 1…
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- The electric field of ?(?) = 1/r + 3(v/m), where r is the distance from the origin, is applied in a region of space. Find the electric potential between the two points ?1=0,5 m and r2 =2 m . Hint: you will have to use integration here, with r1 and r2 as your bounds of integration3. Consider the vector field F F(x, y, z) = sin yi + x cos yî + – sin zk. (a) Show this vector field is conservative. (b) For this vector field, find a potential function o which satisfies (0, 0,0) = 2020.3. Given the following scalar potentials (V), calculate the solution for the gradient of V (VV), and plot the vector arrow representation of this vector field over the given limits. (a) V = 15 + r cos o, for 0 < r < 10, and 0 < $ < 2n. (b) V = 100 + xy, for –10 < x < 10,
- How did you solve D? Wouldn't it's distance be different from that of Point 1 to Point 2 as would be Point 3 to Point 2 and shouldn't that effect the answer for work needed to be done?Find the force vector F on an object of mass m the uniform gravitational field when it is at height z = 0. The +z direction is up. Express vector force in terms of m, z. g. and k, where k is the unit vector in the +z direction. To create the k character: In the equation editor window, select "More", then select "Vectors", and you will find what you need. To write out a vector: for example, if the answer has both x and y components, you would answer in the format Fi + Fj F(z) = -mgk Now find the gravitational potential energy U(z) of the object when it is at an arbitrary height z. Take zero potential to be at position z=0. Keep in mind that the potential energy is a scalar, not a vector. Express U(z) in terms of m. z. and g. U(2)= In what direction does the object accelerate when released with initial velocity upward? downward Oupward or downward depending on the initial mass m. upward or downward depending on the initial velocity upward Now consider the analogous case of a particle…Please explain An electrically charged particle is held fixed at the origin. Let V = 1/r be the potential energy of a second particle with unit electric charge located at (x, y, z), where r = sqrt(x^2 + y^2 + z^2). The force on this second particle is given by −∇V . Calculate the force on the particle when it is at (1, 2, −2). Show working
- What is the potential difference V(r) – V(0) for r < a (i.e., where r is inside the insulating sphere, and V(0) is the potential at the origin)?•prove that the force is Conserved • then find the potential functionRank the potential energies of the four systems of particles shown in the figure below from largest to smallest. Include equalities if appropriate. (Use only ">" or "=" symbols. Do not include any parentheses around the letters or symbols.)