Physics I

FINAL REVISIONSheet I

Prepared byDr. Mohamed Abbas

Content1- Electric Field Electric Force.2- Electric potential Potential energy 3- Gauss law.4- Electric Capacitors.5- Electric resistors - DC circuit.6- Magnetic field Magnetic force.7- Waves.8- Converts.

Electric Field Electric Force:Rules and units F= ma(Coulombs law)Fe is the Electric force (N)m is the mass (kg)a is the acceleration (m/sec2)Q is the charge (C)r is the distance (m)E is the Electric field (N/C)R is the sphere radius (m) is the volume charge density (C/m3) is the surface charge density (C/m2) is the linear charge density (C/m)V is the volume (m3)A is the area (m2)L is the length (m)K = 8.99 x 109 (constant) = 8.85 x 10-12 (constant)

(for a single charge) (for a charged ring) (for a charged infinite sheet)

Problem 1:Three point charges are located on a circular arc as shown in Figure (a) what is the total electric field at P, the center of the arc? (b) Find the electric force that would be exerted on a 25nC point charge placed at P.

Problem 2:A point charge +2Q is at the origin and a point charge -Q is located along the x axis at x = d as in Figure. Find a symbolic expression for the net force on a third point charge Q located along the y axis at y = d.

Problem 3:Three point charges lie along a circle of radius r at angles of 30o, 150o, and 270o as shown in Figure for q=2nC and r =2m. Find the resultant electric field at the center of the circle.

Problem 4:A rod 14cm long is uniformly charged and has a total charge of -22C. determine (a) the magnitude and (b) the direction of the electric field along the axis of the rod at a point 36cm from its center.

Problem 5:A uniformly charged ring of radius 10.0 cm has a total charge of 75C. find the electric field on the axis of the ring at (a) 1cm, (b) 5cm, (c) 30.0 cm, and (d) 100cm from the center of the ring.

Electric potential Potential energyRules and units V is the potential difference (Volt)d is the distance (m)U is the electric potential energy (Joule)W is the work done (Joule).KE is the kinetic energy (Joule).m is the mass (kg)v2 is the velocity (m/sec)

Problem 1:The two charges in the figure are separated b d=2cm. Find the electric potential at (a) point A and (b) point B, which is halfway between the charges.

Problem 2:The two charges in Figure are separated by a distance d=2cm, and Q=15nC. Find (a) the electric potential at A, (b) the electric potential at B, and (c) the electric potential difference between B and A.

Problem 3:The three charged particles in the figure are at the vertices of an isosceles triangle (where d=2cm). Taking q=7.00C, calculate the electric potential at point A, the midpoint of the base.

Problem 4:Calculate the energy required to assemble the array of charges shown in the figure, where a = 0.2m, b = 0.4m, and q = 6C.

Problem 5:An electron moving parallel to the x axis has an initial speed of 3.70X106m/s at the origin. Its speed is reduced to 1.40 X105m/s at the point x=2cm. Calculate the potential difference between the origin and that point. Which point is at the higher potential?

Problem 6: Given two particles with 2C charges, as shown in the figure, and a particle with charge q = 1.28x10-18C at the origin, (a) what is the net force exerted by the two 2C charges on the test charge q? (b) What is the electric field at the origin due to the two 2C charges? (c) What is the electric potential at the origin due to the two 2C charges?

Electric CapacitorRules and units C is the capacitance (Farad)K = constant = 9x109VT is the total p.d (volt)QT is the total charge (C)Vo is the p.d without dielctric materialU is the total energy stoared in the capacitor (J)k is the dielectric constant (No unit). is the permittivity (C.N/m2)Qi is the induced charge (C).Eo is the electric field in absence of dielectric material (N/C)

= For the series combination of capacitors For the parallel combination of capacitors:

Problem 1:Two capacitors, C1=5F and C2=12F, are connected in parallel, and the resulting combination is connected to a 9V battery. Find (a) the equivalent capacitance of the combination, (b) the potential difference across each capacitor, and (c) the charge stored on each capacitor.

Problem 2:Four capacitors are connected as shown in Figure. (a) Find the equivalent capacitance between points a and b. (b) Calculate the charge on each capacitor, taking Vab =15V.

Problem 3:Consider the circuit shown in the figure, where C1=6F, C2=3F, and V=20V. Capacitor C1 is first charged by closing switch S1. Switch S1 is then opened, and the charged capacitor is connected to the uncharged capacitor by closing S2. Calculate (a) the initial charge acquired by C1 and (b) the final charge on each capacitor.

Problem 4:Find the equivalent capacitance between points a and b in the combination of capacitors shown in the figure below.

Problem 6:A parallel-plate capacitor in air has a plate separation of 1.50cm and a plate area of 25.0cm2. The plates are charged to a potential difference of 250V and disconnected from the source. The capacitor is then immersed in distilled water. Assume the liquid is an insulator. Determine (a) the charge on the plates before and after immersion, (b) the capacitance and potential difference after immersion, and (c) the change in energy of the capacitor.

Electric resistors & DC circuits.Rules and unitsI is the electric current (Ampere)V is the potential difference (Volt)Q is the charge (Coulomb)t is the time (sec)W is the work done (Joule)R is the electric resistor ()r is the internal resistance () is the material resistivity (.m). is the conductivity (-1.m-1). P is the electric power (watt)T is the temperature (Celsius)

(at a node) V = 0(at a close loop)

Problem 1:A certain light bulb has a tungsten filament with a resistance of 19.0 V when at 20.0C and 140 V when hot. Assume the resistivity of tungsten varies linearly with temperature even over the large temperature range involved here. Find the temperature of the hot filament.

Problem 2:An aluminum rod has a resistance of 1.23V at 20.0C. Calculate the resistance of the rod at 120C by accounting for the changes in both the resistivity and the dimensions of the rod. The coefficient of linear expansion for aluminum is 2.40 3 1026 (C)-1.

Problem 3:Suppose your portable DVD player draws a current of 350 mA at 6.00 V. How much power does the player require?

Problem 4:Consider the circuit shown in figure below. Find (a) the current in the 20.0-V resistor and (b) the potential difference between points a and b.

Problem 5:For the circuit shown in the fig below, we wish to find the currents I1, I2, and I3. Use Kirchhoffs rules.

Problem 6:In the figure below, find (a) the current in each resistor and (b) the power delivered to each resistor.

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