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. : "Electrostatics"

Electrostatics: Dielectric and Polarization

Q- Two parallel conducting plates are separated by distance d and the potential difference between them is V. A dielectric slab of dielectric constant k and uniform thickness nearly d is inserted between the plates. As the dielectric slab is not smooth enough, it touches the plates in some regions a…

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Electrostatics: Coulomb's Law

Q- Two equally charged point mass of mass m each are suspended from a point by massless threads of length L. In equilibrium position each thread makes and angle ɵ with vertical.

(a) Find the ratio of magnitudes of horizontal electric force and vertical gravitational force on a the masses.

(b) Wh…

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Electrostatics: Flux

Q. A point charge Q is on the axis of a short cylinder at its center. The diameter of the cylinder is equal to its length L (Fig.). What is the total flux through the curved sides of the cylinder?

Solution: 

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Linear Charge Density

(On request- Harsh)

Q- (a) Linear charge density of a half ring varies with θ as λ = λ0 cos θ. Find total charge on the ring.

    (b) If the linear charge density of a wire of length L depends on the distance x from its one end as λ=λ0x/L, find total charge of the wire.

Solution:

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Electrostatics

(On request - Nshwah)

Q- Two charges are placed between the plates of a parallel plate capacitor. One charge is +q1 and the other is q2 = +6.58 mC. charge per unit are on each plate has a magnitude of σ = 1.39*10-4 C/m2. If the magnitude of force on q1 due to q2 is equal to that on q1 due to the …

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Electric Flux

(On request - Nshwah)

Q- Figure shows top view of two surfaces intersecting at right angle. Surface 1 has an area of 1.5 m2 and that of the surface 2 is 3.3 m2. Uniform electric field E of strength 270 N/C is making angle 35o with surface 2. Find electric flux through

(a) Surface 1

(b) Surface 2

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Electrostatics: Coulomb's Law

Q- Three charges are fixed in place as shown. The squares in the grid have sides of length s = 0.24 m. The magnitude of q is 3 µC while the magnitude of Q is 4.5 µC. What is the magnitude of the net force on q due to the other two charges?

Solution:

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Electrostatics: Field

Q- Two charges q = -2 µC and Q = +4µC are placed at a distance d = 12 cm from each other. Find position of a point along the line joining the charges where the electric field is zero. 

Solution:

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Electrostatics: Field in Cavity

Q. A sphere of radius r0 carries a volume charge density ρE. A spherical cavity of radius r0/2 is then scooped out and left empty, as shown. 

(a) What is the magnitude and direction of the electric field at point A? 

(b) What is the direction and magnitude of the electric field at point B? Poin…

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Capacitors

Q- Two capacitors are connected to a battery with a two way swatch, as shown in figure. The capacitors are initially uncharged. When the switch is thrown to the left the capacitor C1 = 10 µF is charged to 50 V. Now the switch is thrown to the right and the voltage across C1 is drops to 35 V.

(a)…

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Coulomb's Law: Force and Field

Q- Four charges q1 = q3 = - q and q2 = q4 = + q, where q = 7 µC, are fixed at the corners of a square with sides a = 2.2 m, as in figure.

(a) Calculate the x- and y-components of the net electric field at the midpoint M of the bottom side of the square.

(b) Find the total force exerted on q4 by…

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Coulomb's Law

Q- Six point charges, four positive (+q) and two negative (-q), are fixed at the positions shown in the x-y plane; q = 2 × 10-6 C and a = 0.88 m. A test charge Q = 1.5 × 10-6 C is at the origin. Find the x- and y-components of the total force on Q.

Solution:

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Electrostatics: Field and Force

Q- Throughout space there is a uniform electric field in the - y direction of strength E = 550 N/C. There is no gravity. At t = 0, a particle with mass m = 2 g charge q = -11 µC is at the origin moving with a velocity v0 = 45 m/sat an angle q = 25° above the x-axis.

(a) What is the magnitude of …

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Coulomb's Law: Force and Field

Q- Two charges placed on the x axis. Qa = 4 µC at x = 0 and Qb = - 4 µC at x = 22cm.

(a) Find the net electric field at point P at x = - 6 cm. 

(b) Find the force on Qb due to Qa

(c) The charges Qa and Qb are now attached to the ends of a spring whose un-stretched length is s0 = 22 cm and…

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Electrostatics: Capacitors

Q- Two capacitors C1 = 30 µF and C2 = 60 µF are connected in series with a 12 V battery. Find

(a) The charge on C1 and

(b) The potential difference across C2.

Solution:

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Capacitor

Q- A capacitor stores 135 J of energy when it is charged to 300 V

(a) What is the capacitance of the capacitor?

(b) How much charge must be transferred from one plate to the other to store this energy? 

Solution:

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Electrostatics: Electric Field

Q- Three charges are placed at the vertices of an equilateral triangle of side a = 6 cm. qA = +3 µC, qB = +3 µC, and qC = -3 µC.

(a) Find the x- and y- components of the electric force acting on qC

(b) Find the electric field at the position of qC due to qA and qB.

Solution:

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Electrostatics: Coulomb's Law

Q- Two charges Qc and -Qc (Qc = 4 µC) are fixed on the x-axis at x = -6 cm and x = 6 cm, respectively. A third charge Qb = 5 µC is fixed at the origin. A particle with charge q = 0.5 µC and mass m = 6 g is placed on the y-axis at y = 14 cm and released. There is no gravity. Calculate the initial …

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Electrostatics: Capacitors

Q- Determine the equivalent capacitance of the combination shown in figure where a = 10C and b = 45C

Solution:

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Electrostatics: Coulomb's Law

Q- A rigid, insulating fiber if fixed vertically. A charge Qa = -7 µC is fixed to the fiber at some point. A bead with a hole drilled through its center is slipped over the fiber above Qa and is free to move along the fiber without friction. The mass of the bead is m = 160 g and its charge is Qb. A…

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