A nonuniform linear charge distribution given by λ(x) = bx, where b is a constant, is...

A nonuniform linear charge distribution given by λ(x) = bx, where b is a constant, is distributed along the x axis from x = 0 to x = +L. If b = 40 nC/m and L = 0.67 m, what is the electric potential (relative to a potential of zero at infinity) at the point y = 2L on the y axis?

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genius_generous answered 2 years ago

y''−2xy' + λy = 0, −∞ < x < ∞ where λ is a constant, is...

y''−2xy' + λy = 0, −∞ < x < ∞ where λ is a constant, is known as the Hermite equation, named after the famous mathematician Charles Hermite. This equation is an important equation in mathematical physics. • Find the ﬁrst four terms in each of two solutions about x = 0 and show that they form a fundamental set of solutions • Observe that if λ is a nonnegative even integer, then one or the other of the series...

A solid nonconducting sphere of radius R = 5.5 cm has a nonuniform charge distribution of...

A solid nonconducting sphere of radius R = 5.5 cm has a nonuniform charge distribution of volume charge density ρ = (15.4 pC/m3)r/R, where r is radial distance from the sphere's center. (a) What is the sphere's total charge? What is the magnitude E of the electric field at (b) r = 0, (c) r = R/2.0, and (d) r = R?

A solid nonconducting sphere of radius R = 5.7 cm has a nonuniform charge distribution of...

A solid nonconducting sphere of radius R = 5.7 cm has a nonuniform charge distribution of volume charge density ρ = (14.4 pC/m3)r/R, where r is radial distance from the sphere's center. (a) What is the sphere's total charge? What is the magnitude E of the electric field at (b) r = 0, (c) r = R/2.0, and (d) r = R?

Question: (Bayesian) Suppose that X is Poisson(λ + 1), and the prior distribution of λ is...

Question: (Bayesian) Suppose that X is Poisson(λ + 1), and the prior distribution of λ is binomial(2,1/3). (a) Find the Bayesian estimate of λ for mean square loss based on the single observation X, if X = 1. (b) Find the Bayesian estimate of λ for mean square loss based on the single observation X, if X = 2 Hints: Because of its prior distribution, λ can take only three values, 0,1,2. Don’t expect its posterior distribution to be any...

Given, op: (λ(n) (λ(f) (λ(x) (((n (λ(g) (λ(h) (h (g f))))) (λ(u) x)) (λ(u) u))))) zero:...

Given, op: (λ(n) (λ(f) (λ(x) (((n (λ(g) (λ(h) (h (g f))))) (λ(u) x)) (λ(u) u))))) zero: (λ(f) (λ(x) x)) one: (λ(f) (λ(x) (f x))) two: (λ(f) (λ(x) (f (f x)))) three: (λ(f) (λ(x) (f (f (f x))))) i. (4 pt) What is the result of (op one)? ii. (4 pt) What is the result of (op two)? iii. (4 pt)What is the result of (op three)? iv. (3 pt) What computation does op perform?

Consider the ODE y''(x) = λy(x) for some real constant λ. Determine ALL values of λ...

Consider the ODE y''(x) = λy(x) for some real constant λ. Determine ALL values of λ for which there exists solutions satisfying the boundary conditions y(0) = y(10) = 0. For each such λ, give all possible solutions. Are they unique?

Prove the Following: Where a and b are constants. a). Σ(?−?̅)=0 b). Var( a + bX)...

Prove the Following: Where a and b are constants. a). Σ(?−?̅)=0 b). Var( a + bX) = b2Var(X)

A line of charge (with charge per unit length given by λ) extends from (0,0,0) along...

A line of charge (with charge per unit length given by λ) extends from (0,0,0) along the x axis to infinity. Answer the following 2 questions about the electric field at the point (x,y,z) = (0,a,0). A correct integral expression for the y component of the electric field at this point is given by which of the following? In each case the integral has limits 0 and ∞. λ/(4πε0)∫dx a/(a2 + x2)3/2 k λ/(4πε0)∫dx a/(a2 + x2)3/2 j λ/(4πε0)∫dx a/(a2...

A force F = −F0 e ^−x/λ (where F0 and λ are positive constants) acts on...

A force F = −F0 e ^−x/λ (where F0 and λ are positive constants) acts on a particle of mass m that is initially at x = x0 and moving with velocity v0 (> 0). Show that the velocity of the particle is given by v(x)=(v0^2+(2F0λ /m)((e^-x/λ)-1))^1/2 where the upper (lower) sign corresponds to the motion in the positive (negative) x direction. Consider first the upper sign. For simplicity, define ve=(2F0 λ /m)^1/2 then show that the asymptotic velocity (limiting...

Given is the rod of length L with the linear charge of density ?=?/? . The...

Given is the rod of length L with the linear charge of density ?=?/? . The rod lies on the x axis with its midpoint at the origin. Find the electric field vector on y axis resulting from such continuous system of charge at distance y from the origin. Use this result to obtain the expression for electric field at distance y from the infinitely long wire.

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