How Much Energy Is Required to Move a Charge to Infinity?

[mustang]

Problem 10.
Given: k_e=8.98755*10^9 nm^2/C^2 and g=9.8 m/s^2.
Three charges are at three corners of a rectangle a charge of +8.6uC is at the upper left hand corner, a +2.5uC is at the lower left hand corner, and a +3.7 uC is ath the lower right hand corner. The length of the rectangle is 5.1 cm and the width is 3.1 cm.
How much electrical potential energy would be expended in moving the 8.6 uC charge to infinity? Answer in units of J.

Problem 11.
Given: k_e=8.98755*10^9 nm^2/C^2 and g=9.8 m/s^2.
Three charges are located at the vertices of an isosceles triangle. A postive charge is
a the top vertice, and two negative charges are at the bases. The length of the base is 2.7 cm and the other two sides is 5.4 cm.
Calculate the electric potential at the midpoint of the base if the magnitude of each charge is 3.9*10^-9C. Answer in units of V.
note: What formula would you use?

Problem 18.
A parallel-plate capacitor has a capacitance of 0.25 uF and is to be operated at 6300 V.
What is the electrial potential energy stored in the capacitory at the operating potential difference? Answer in units of J.
Note: I don't know where to start.

 

[himanshu121]

Calculate the potential(V) at the point where a charge of 8.6uC is located due to the other two charges. At infinity the potential due to other charges will be zero

Therefore Electric Potential Energy is = q(V-0)

2) Potential at a point due to charge q is kq/r where r is the distance b/w the charge and the point where potential is to be calculated

3) apply the formula 1/2 CV^2

 

[M98Ranger]

For Problem 10:

To solve this problem, we can use the formula for electrical potential energy: U = k_e * (q1*q2)/r, where k_e is the Coulomb's constant, q1 and q2 are the charges, and r is the distance between the charges.

First, we need to find the distance between the +8.6uC charge and infinity. Since the charge is moving to infinity, we can assume that the distance is very large, approaching infinity. Therefore, we can use the limit as r approaches infinity, which is equal to zero.

Plugging in the given values, we get: U = (8.98755*10^9 nm^2/C^2) * (8.6*10^-6 C * 0 C)/0 = 0 J.

Therefore, no electrical potential energy would be expended in moving the +8.6uC charge to infinity.

For Problem 11:

To solve this problem, we can use the formula for electric potential: V = k_e * (q/r), where k_e is the Coulomb's constant, q is the charge, and r is the distance between the charge and the point where we want to find the potential.

In this case, we need to find the potential at the midpoint of the base, which is half the distance of the base. Therefore, r = 1.35 cm.

Plugging in the given values, we get: V = (8.98755*10^9 nm^2/C^2) * (3.9*10^-9 C/1.35 cm) = 10.46 V.

The formula used for this problem is the formula for electric potential.

For Problem 18:

To solve this problem, we can use the formula for electric potential energy stored in a capacitor: U = (1/2)*C*V^2, where C is the capacitance and V is the potential difference.

Plugging in the given values, we get: U = (1/2)*(0.25*10^-6 uF)*(6300 V)^2 = 496.125 J.

Therefore, the electrical potential energy stored in the capacitor at the operating potential difference is 496.125 J. The formula used for this problem is the formula for electric potential energy stored in a capacitor.