Magnetic Force and Current Homework Set Problem 1. An electron that is moving through a uniform magnetic field has a velocity v= (40 km/s) i + (35 km/s) j. when it experiences a F = (-4.2 fN) i + (4.8 fN) j due to a magnetic field. If Bx = 0, calculate the magnetic field B. Convert the relevant quantities to SI units. Write the components of the force exerted by an external magnetic field on a particle with velocity components vx, vy, and vz Perform algebraic manipulation and solve for each magnetic field component in terms of the force and velocity components. Use these to find the magnetic field vector.Magnetic Force and Current Homework Set Problem 2. An alpha particle (q = +2e, m=4.00 u) travels in a circular path of radius 4.50 cm in a magnetic field with B= 1.20 T. Calculate a) its speed b) its period of revolution Derive the velocity by setting the centripetal force equal to the force on a charged particle with velocity v in an external magnetic field B. Perform appropriate algebraic manipulation to solve for v. Convert the relevant quantities to SI units. Insert the appropriate quantities and solve for its speed. Derive the period by dividing the circumference of the path by its speedMagnetic Force and Current Homework Set c) its kinetic energy in electron-volts Insert the appropriate quantities and solve for its period. Use its speed and calculate its kinetic energy in joules d) and the potential energy through which it would have to be accelerated to achieve this energy. 1 eV =1.602 x 10-19J Convert the value from joules to electron-volts using the conversion factor of Recall the expression relating potential energy to electric potential. Use the charge of the alpha particle to calculate the electric potential required.Magnetic Force and Current Homework Set Problem 3. A fuse in an electric circuit is a wire designed to melt and thereby open the circuit, if the current exceeds a certain value. Suppose that the material used in a fuse melts when the current density rises to 440 A/cm2. What diameter of cylindrical wire should be used to limit the current to 0.50 A? Convert the relevant information to SI units. Write the expression of current density in terms of current and area of the wire. Write the expression of the cross-sectional area of a wire of radius r. Substitute this expression into the current density and perform algebraic manipulation to solve for r. Insert the relevant information to find a numerical value for r.Magnetic Force and Current Homework Set Problem 4. In a hypothetical fusion research lab, high-temperature helium gas is completely ionized, each helium atom being separated into two free electrons and the remaining positively charged nucleus (the alpha particle). An applied electric field causes the alpha particles to drift to the east at 25 m/s while the electrons drift to the west at 88 m/s. The alpha particle density is 2.8 x 10-15 cm-3. Calculate the net current density; specify the current direction. Convert the relevant information to SI units. Write an expression for the charge carrier density in terms of the amount of charge/carrier and the particle density. Write the expression of the current density in terms of the drift velocity, and the charge carrier density. Calculate the current density of the electrons and alpha particles. Based on the fact that there are 2 electrons for every alpha particle, find the particle density of the electrons. Sum the current densities to find the total current density. Determine the direction by finding the direction of the positive charge carriers.Magnetic Force and Current Homework Set Problem 5. A wire that is 4.00 m long and 6.00 mm in diameter has a resistance of 3.9 mΩ. A potential of 23.0 V is applied between the ends. a) What is the current in the wire? Convert the relevant information to SI units. b) What is the current density? Use the relationship known as Ohm’s law to calculate the current. Calculate the cross-sectional area of the wire. c) Calculate the resistivity of the wire material. Calculate the current density. Write an expression for the resistivity as a function of resistance, wire length and wire area. d) Identify the material using a table in your book. Insert the relevant information and calculate the resistivityMagnetic Force and Current Homework Set Problem 6. If the gauge number of a wire is increased by 6, the diameter is halved; if a gauge number is increased by 1, the diameter decreases by 21/6. This is shown in the table below. Gaugea 4 6 8 10 12 14 16 18 0 50 35 25 20 15 6 3 Diameter, milsb 204 162 129 102 81 64 51 40 Safe Current A 70 50 35 25 20 15 6 3 a A way of identifying wire diameter, b 1 mil= 10-3 in. = 2.53 x 10-3 cm= 2.53 x 10-5 m. Write an expression of proportionality between resistance and ratio of length to area. Based on the 21/6, calculate the ratio of diameter of 22-gauge wire to 10-gauge wire. Use the proportionality relationship to calculate the resistance. (Hint: area is proportional to diameter squared).Magnetic Force and Current Homework Set Problem 7. A 1250 W radiant heater is constructed to operate at 115 V. a) What will be the current in the heater? Write the relationship of power in terms of voltage and current. b) What is the resistance of the heating coil? Perform algebraic manipulation and solve for the current Write the relationship of power in terms of current and resistance. c) How much thermal energy is generated in 1 hour by the heater? Perform algebraic manipulation and solve for the current Convert 1 hour into seconds Show the conversion between watts and joules per second. Calculate the heat generated.Magnetic Force and Current Homework Set Problem 8. A wire 50 cm long lying along the x-axis carries a current of 0.5 A in the positive x direction through a magnetic field of B= (0.0030 T) j + (0.010 T) k. Find the force on the wire. Convert the relevant quantities to SI units. Write the expression that relates the force on a wire in an external magnetic field to its current and length. Evaluate the vector product for each of the components of the magnetic field Insert the relevant quantities and find the vector expression of the force on the wire.Magnetic Force and Current Homework Set Problem 9. A long rigid conductor, lying on the x-axis, carries a current 5.0 A in the negative direction. A magnetic field B is present given by B= 3.0 i + 8.0 x2 j with x in meters and B