Question

The electric field in the xy-plane due to an infinite line of charge along the z-axis is a gradient field with a potential function V(x,y) = c ln (r0 / ?(x^2 + y^2)), where c > 0 is a constant and r0 is a reference distance at which the potential is assumed to be 0. Use this information to answer parts a through c. a. Find the components of the electric field in the x- and y-directions, where E(x,y) = - ?V(x,y). Choose the correct answer below. A. E = (cr0 / ?(x^2 + y^2)) ?x,y? B. E = (c / ?(x^2 + y^2)) ?x,y? C. E = (c / (x^2 + y^2)) ?x,y? D. E = (c / (r0(x^2 + y^2))) ?x,y? The gravitational force on a point mass m due to a point mass M is a gradient field with potential U(r) = -GMm / r, where G is the gravitational constant and r = ?(x^2 + y^2 + z^2) is the distance between the masses. Answer parts a through c. a. Find the components of the gravitational force in the x-, y-, and z-directions, where F(x,y,z) = - ?U(x,y,z). Choose the correct answer below. A. F(x,y,z) = (GMm / (x^2 + y^2 + z^2)) ?x,y,z? B. F(x,y,z) = (GMm / (x^2 + y^2 + z^2)^(3/2)) ?x,y,z? C. F(x,y,z) = (GMm / (x^2 + y^2 + z^2)^2) ?x,y,z? D. F(x,y,z) = (GMm / ?(x^2 + y^2 + z^2)) ?x,y,z?

          The electric field in the xy-plane due to an infinite line of charge along the z-axis is a gradient field with a potential function V(x,y) = c ln (r0 / ?(x^2 + y^2)), where c > 0 is a constant and r0 is a reference distance at which the potential is assumed to be 0. Use this information to answer parts a through c.
a. Find the components of the electric field in the x- and y-directions, where E(x,y) = - ?V(x,y). Choose the correct answer below.
A. E = (cr0 / ?(x^2 + y^2)) ?x,y?
B. E = (c / ?(x^2 + y^2)) ?x,y?
C. E = (c / (x^2 + y^2)) ?x,y?
D. E = (c / (r0(x^2 + y^2))) ?x,y?
The gravitational force on a point mass m due to a point mass M is a gradient field with potential U(r) = -GMm / r, where G is the gravitational constant and r = ?(x^2 + y^2 + z^2) is the distance between the masses. Answer parts a through c.
a. Find the components of the gravitational force in the x-, y-, and z-directions, where F(x,y,z) = - ?U(x,y,z). Choose the correct answer below.
A. F(x,y,z) = (GMm / (x^2 + y^2 + z^2)) ?x,y,z?
B. F(x,y,z) = (GMm / (x^2 + y^2 + z^2)^(3/2)) ?x,y,z?
C. F(x,y,z) = (GMm / (x^2 + y^2 + z^2)^2) ?x,y,z?
D. F(x,y,z) = (GMm / ?(x^2 + y^2 + z^2)) ?x,y,z?

The electric field in the xy-plane due to an infinite line of charge along the z-axis is a gradient field with a potential function V(x,y) = c ln (r0 / ?(x^2 + y^2)), where c > 0 is a constant and r0 is a reference distance at which the potential is assumed to be 0. Use this information to answer parts a through c.
a. Find the components of the electric field in the x- and y-directions, where E(x,y) = - ?V(x,y). Choose the correct answer below.
A. E = (cr0 / ?(x^2 + y^2)) ?x,y?
B. E = (c / ?(x^2 + y^2)) ?x,y?
C. E = (c / (x^2 + y^2)) ?x,y?
D. E = (c / (r0(x^2 + y^2))) ?x,y?
The gravitational force on a point mass m due to a point mass M is a gradient field with potential U(r) = -GMm / r, where G is the gravitational constant and r = ?(x^2 + y^2 + z^2) is the distance between the masses. Answer parts a through c.
a. Find the components of the gravitational force in the x-, y-, and z-directions, where F(x,y,z) = - ?U(x,y,z). Choose the correct answer below.
A. F(x,y,z) = (GMm / (x^2 + y^2 + z^2)) ?x,y,z?
B. F(x,y,z) = (GMm / (x^2 + y^2 + z^2)^(3/2)) ?x,y,z?
C. F(x,y,z) = (GMm / (x^2 + y^2 + z^2)^2) ?x,y,z?
D. F(x,y,z) = (GMm / ?(x^2 + y^2 + z^2)) ?x,y,z?

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