A rod of length L = 4.00 m with uniform charge of 8.10 nC/m is oriented along the y axis as shown in the diagram. P₁ X (a) What is the electric potential at the location P, whose coordinates are (0, -5.50 m)? 1 V (b) What is the electric potential at the location P, whose coordinates are (5.50 m, 2.00 m)?
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- A thin rod extends along the x-axis from x = −a to x = a . The rod carries a positive charge +Q uniformly distributed along its length 2a with charge density λ, as shown in Figure attached. a) Use dV = 1/4πε0 ∫ dq/r to show that the electric potential at point P is given by: V(x) = (λ/4πε0) ln(x + a/x − a) b) What is the electric potential of the rod at x = 4a and x = 2a? c) What is the electric potential difference between x = 4a and x = 2a?The thin plastic rod of length L = 18.2 cm in the figure has a nonuniform linear charge density λ= cx, where c= 24.8 pC/m. (a) With V=0 at infinity, find the electric potential at point P₂ on the y axis at y D=4.90 cm. (b) Find the electric field component Ey at P₂. (a) Number i (b) Number i D d- Units V Units V/mTwo concentric spherical conductive shells of radii 5 cm and 10 cm are charged with 6 µC and 1 µC, respectively. What is the electric potential at r=0, r=7.5cm, and r=15cm? V1= Enter a number. ix V, V2= V, V2= V.
- An infinitely long metal cylinder has radius R0 and charge per unit length λ. It is held at potential V0, which you should use as the reference point for this problem. The cylinder is solid (not hollow) and in electrostatic equilibrium. (a) Find the electric potential outside the cylinder, for a distance r > R0 from the center of the cylinder. (b) Find the electric potential inside the cylinder, at a distance r < R0 from the center of the cylinder.V(x) The 10V А В DE 1V 0 1 2 3 4 5 6 (cm) graph shows the potential V as a function of position x. Please consider the electric fields in the five regions, A through E for the following questions. In which region does the direction of the electric field point left: Submit Answer Tries 0/2 The magnitude (i.e. absolute value) of the electric field in region A is: V/m Submit Answer Tries 0/2 The magnitude (i.e. absolute value) of the electric field in region B is: V/mA plastic rod has been bent into a circle of radius R = 9.53 cm. It has a charge Q1 = +4.81 pC uniformly distributed along one-quarter of its circumference and a charge Q2 = -6Q1 uniformly distributed along the rest of the circumference (see the figure). With V = 0 at infinity, what is the electric potential (a) at the center C of the circle and (b) at point P, which is on the central axis of the circle at distance D = 3.61 cm from the center?
- A plastic rod has been bent into a circle of radius R = 11.0 cm. It has a charge Q1 = + 5.38 pC uniformly distributed along one-quarter of its circumference and a charge Q2 = -6Q, uniformly distributed along the rest of the circumference (see the figure). With V = 0 at infinity, what is the electric potential (a) at the center C of the circle and (b) at point P, which is on the central axis of the circle at distance D = 6.02 cm from the center? D Q2 (a) Number i -2.2 Units V (b) Number -1.93 UnitsA ring of radius R = 4cm lies in the y-z plane and is centered at the origin. The ring carries a uniform charge Q = 48μC. A point P is located along the x-axis a distance x = 3.9 cm from the origin. The equation for electric potential at point P due to charge on the ring can be represented as V = (kQ)/(R2+x2)0.5. Using the equation for electric potential as a function of x, derive an equation for the electric field along the positive x-axis. Give the answer in terms of the variables Q, R, x, and Coulomb constant k. Calculate the magnitude of the elctric field at point P in units of meganewtons per coulomb (MN/C)A solid aluminum sphere with radius a has an explicitly negative charge,−q. Concentric with the aluminum sphere is a copper spherical shell with inner radius b, outer radius c, and an explicitly positive charge, +Q. Assume that the magnitude of the positive charge on the copper shell is greater than the magnitude of the negative charge on the aluminum sphere, and take the electric potential at infinity as zero. Enter an expression for the electric potential, V, that is valid for a