Find the electrostatic potential inside a tube of infinite length along the axis z and whose cross section is a square of side a in the xy plane; as shown in figure, three of sides are grounded to zero, while the top face, at y = a, has a constant potential Vo. y, V(x.y=a)=V_ V(x=0,y)=0 V(x=a,y)=0 V(x.y=0)=0

o A B KR/2 A very long, solid insulating cylinder of radius R = 1m has a cylindrical empty hole with radius R/2 centered at O' along its entire length. The solid material of the cylinder has a unifom volume charge density p = 3x10-9. The di stance between O' and A points is R/4 and the Point B is 10R away from the point O. What is the potential difference between points A and B, that is, VA-VB? = 8.85x10-12 (C²/N.m²)). m2 A) 536.1 V B) 178.7 V C) 571.8 V D) 64.33 V E) 128.6 V

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A charge Q field E and the electrostatic potential at rı 10-10C is uniformly distributed on a sphere of radius R= 10cm. What is the valued of the electric R. , r2 = R, r3 = 2R from the center of the sphere?

Two coaxial cones are described as 0 = 10° and 0 = 30°. If potential on cones at 0 = 10° and 0 = 30° are 100 V and 0 V, respectively, i. Find voltage at 0 = 20°. ii. Determine angle 0 for which potential is 50 V. Consider that the cone vertices are insulated at r = 0.

A 9V battery is connected between an inner spherical conductor (R₁ = 10 cm) and a concentric conducting spherical shell (R2 = 30 c m, R3 = 35 cm,). The inner spherical conductor is positively charged (+Q) and the outer conducting spherical shell is negatively charged (-Q). Find the potential at a point, r, between the conductors where the electric potential of the outer conducting spherical shell is set to zero as the reference. O R₂ v(r) = v(r) = R₂ R₁ Q Απερ Q 4πε r 1 (1/1₂ - +) V(x) = R. 1 R Q Απε R 0 V (1) = - =-(- - - - -) Q 1 1 V(r) 4πε r R

The vertical deflecting plates of a typical classroom oscilloscope are a pair of parallel square metal plates carrying equal but opposite charges. The potential difference between the plates is 25.0 V. Typical dimensions are about 3.3 cm on a side, with a separation of about 5.0 mm. The plates are close enough that we can ignore fringing at the ends. Part A:Under these conditions, how much charge is on each plate? Q=__C Part B:How strong is the electric field between the plates? E=__V/m Part C:If an electron is ejected at rest from the negative plates, how fast is it moving when it reaches the positive plate?v=__m/s

Four equal positive charges, of magnitude 10-6 C are situated at the corners of a square, with a length of side equal to 0.25m. A small test charge of 10-9 C is placed at location X, in the exact center of the square. What is the magnitude of the potential energy of the test charge and what is the voltage at X? If the test charge is released what is its final velocity, taking its mass to be 1.5g?

A uniform electric field of magnitude 280 V/m is directed in the negative y direction as shown in the figure below. The coordinates of point A are (-0.900, -0.200) m, and those of point ® are (0.500, 0.450) m. Calculate the electric potential difference Va - V, using the dashed-line path. A

On a square wireframe with side length a in empty space, there is a linear charge density ρl. Calculate a · ρl numerically by finding a solution for the values of a and ρl required for the potential at the center of this square frame to be V = 2 ke [Volts].