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A wire carries a current of 22.0 A from West to East. Assume that at this location the magnetic
field of Earth is horizontal and directed from south to north and that it has a magnitude of
0.500 x 10-4 T.
(a) Find the magnitude and direction of the magnetic force on a 36.0-m length of wire.
(b) Calculate the gravitational force on the same length of wire if it’s made of copper and has a
cross-sectional area of 2.50 x 10-6 m2.
Date posted:
May 12, 2021
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A proton moves at 8.00 x 106 m/s along the x-axis. It enters a region in which there is a magnetic
field of magnitude 2.50 T, directed at an angle of 60.0° with the x-axis and lying in the xy - plane
(Fig. 4.3). Find the initial magnitude and direction of the magnetic force on the proton.
Date posted:
May 12, 2021
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The Earth's magnetic field is about 50 μT northward. Find the velocity that an electron moving
westward would have so that the magnetic force balances gravity.
Date posted:
May 12, 2021
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A battery, a capacitor and a resistor are connected as shown in figure below. Obtain an expression
for the charge after the switch is closed.
When switch is closed at 1, capacitor charging and when at position 2, the capacitor is
discharging.
Date posted:
May 12, 2021
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A charge q1 = 2.00 μC is located at the origin, and a charge q2 = -6.00 μC is located at (0, 3.00)
m, as shown in figure a.
(a) Find the total electric potential due to these charges at the point P, whose coordinates are
(4.00, 0) m.
(b) Find the change in potential energy of a 3.00 μC charge as it moves from infinity to point P
of (Fig a) such that the situation is as in Fig b.
Date posted:
May 11, 2021
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Two large, parallel, conducting plates are 12 cm apart and have charges of equal magnitude and
opposite sign on their facing surfaces. An electrostatic force of 3.9 x 10-15 N acts on an electron
placed anywhere between the two plates (Neglecting fringing)
(a) Find the electric filed at the position of the electron
(b) What is the potential difference between the plates?
Date posted:
May 11, 2021
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A rod of length l has a uniform positive charge per unit length λ and a total charge Q. Calculate the electric field at a point P that is located along the long axis of the rod and a distance a from one end.
Date posted:
May 11, 2021
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A charge q1 = 7.0 μC is located at the origin, and a second charge q2 = -5.0μC is located on the x
axis, 0.30 m from the origin. Find the electric field at the point P, which has coordinates (0, 0.40) m.
Date posted:
May 11, 2021
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Two particles are fixed to an x- axis: particle 1 of charge -2.1 x 10-8 C at x = 20 cm and particle 2
of charge q2 = -4.00q1 at x = 70 cm. At what coordinate on the axis is the net electric field
produced by the particles equal to zero?
Date posted:
May 11, 2021
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What is the magnitude of a point charge whose electric field 50 cm away has a magnitude of 2.0 N/C?
Date posted:
May 11, 2021
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Three point charges lie along the x axis as shown in figure 2.2. The positive charge q1 =15.0μC is
at x = 2.00 m, the positive charge q2 = 6.00 μC is at the origin, and the resultant force acting on
q3 is zero. What is the x coordinate of q3?
Date posted:
May 11, 2021
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Consider three point charges located at the corners of a right triangle as shown in figure 2.1, where q1= q3 = 5.0 μC, q2 = -2.0 μC and a = 0.10 m. Find the resultant force exerted on q3.
Date posted:
May 11, 2021
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The electron and proton of a hydrogen atom are separated (on the average) by a distance of approximately 5.3 x 10-11 m. Find the magnitudes of the electric force between the two particles.
Date posted:
May 11, 2021
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How much charge is represented by 4,600 electrons?
Date posted:
May 11, 2021
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Find the currents l1, l2, and l3 in the circuit shown in figure below.
Date posted:
May 11, 2021
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Find the current I in the circuit of the figure below.
Date posted:
May 11, 2021
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The terminal p.d of a battery is 12 V when an external resistance of 20 Ω is connected and 13.5 V when an external resistance of 45 Ω is connected. Calculate the emf and internal resistance of the battery.
Date posted:
May 11, 2021
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A battery of emf 40 V and internal resistance 5 Ω is connected to a resistance of 15 Ω.
Calculate the terminal p.d.
Date posted:
May 11, 2021
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A cell of unknown emf E and internal resistance 2 Ω is connected to a 5 Ω resistance. If the terminal p.d V is 1.0 V, calculate E.
Date posted:
May 11, 2021
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Explain the difference between load resistance in a circuit and internal resistance in a battery.
Date posted:
May 11, 2021
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Four resistors are connected as shown in figure below.
(a) Find the equivalent resistance between points a and c.
(b) What is the current in each resistor if a potential difference of 42 V is maintained between a and c ?
Date posted:
May 11, 2021
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Consider five resistors connected as shown in figure below. Find the equivalent resistance between points a and b.
Date posted:
May 11, 2021
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Define current density and show how it is related to drift velocity.
Date posted:
May 11, 2021
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Solomon's Limited sells an electric calculators but finds that it runs our of stock
on occasions and thus loses the contribution on missed sales. The estimated demand is 12,000
units per year which can be purchased at shs100 each and sold at Shs 155 each. The lead-time is
5 days guaranteed and the cost of holding a calculator is sh20 per year. The company's
economic order quantity is 1,200 calculators. Solomon's Limited works a five-day
week for 48 weeks a year. The demand figures have been analyzed for the last 27 weeks;
At present Solomon's Limited uses a re-order level of 2,500 calculators and does not
carry any safety stock because of the guaranteed delivery time. Ideally it wishes to satisfy
customers on average at least 95% of the time whilst minimizing the associated costs.
Required:
1. The annual stock-out costs of using the present re-order level.
2. The re-order level at which the company would meet it's 95% requirement.
Date posted:
May 10, 2021
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Chopa manufacturers limited operate 30-day terms for all its customers. Experience has
shown that 80% of all accounts are settled within one month and 70% of the remainder is
settled during the second month after the customer has been sent a standard overdue
account letter of those accounts still unpaid after two months. 50% are settled during the
third month after a 'final demand' has been sent. Any accounts still not paid after
three months are dealt with in one of two ways. If the amount owing exceeds shs 1 million,
the Company institutes legal proceedings to recover the money. Taking into account the
legal costs involved, the proportion of the original sum owing, which is ultimately recovered
varies as follows;
Required:
What is the probability that, for any particular account, payment is received at the end of:
(i) The second month
(ii) The third month
(iii) The fourth month
(iv) The sixth month
b) What is the expected present value of a new account which has Shs 2 million outstanding.
Monthly Discount factors are;
Month 1 2 3 4 5 6
Factor 0.9852 0.9707 0.9563 0.9422 0.9283 0.9145
(c) Show how the system as a whole may be simulated by using the
following random digits to determine the present value of two simulated accounts.
Account 1 8 8 7 5 7
Account 2 9 98 2 9
Date posted:
May 10, 2021
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Yoloks molders limited had orders to be completed next week for three of its products A, B, C as given the table below:
Required:
i. Use the transportation model to find the minimum cost production schedule for the
products and machines. Determine minimum cost.
ii. If this optimal solution is not unique, describe all other production schedule with the
minimum cost. If the production manager would like the minimum cost schedule to
have the smallest number of changeovers of production on machines, recommend the
optimal solution.
Date posted:
May 10, 2021
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In transportation problems the following difficulties do occur;
degeneracy, inequality of supply and demand and non - unique optimal solution.
Required:
(i) Explain the underlined words.
(ii) Explain how the transportation algorithm is adapted to overcome the above difficulties.
Date posted:
May 10, 2021
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Minwa Tods Limited purchases a large number of wooden pullets for use in the storage and
transportation of its products to replace those cost or damaged in transit. The average yearly
requirement for the past 3 years has been 6,000 pullets. A quantity, which can be applied
realistically to this year as well. The need for replacement pullets is relatively constant and
the cost associated with the placing and receipt of an order is Shs30.
The inventory cost policy that Minwa Tods ltd has traditionally employed is to charge 22%
of the purchase cost as the annual inventory holding cost for any item in the inventory. The
standard price charged by the major manufacturing company is Shs16 per pallet.
Required:
a) Determine the optimum order quantity and the consequent time between orders
b) Describe the assumptions you have made in part (a) and assess their likely validity within
the context of this question.
c) The manufacturer offers a discount of 4% if Minwa Tods order 4,000 or more pullets
at a time. Show that the discount is not financially beneficial to Minwa Tods. What
percentage discount would be required for Minwa Tods to order 4,000 or more
pullets at a time?
d) State the effect on the company‟s inventory policy described in (a) if
the supply of pullets has a variable lead-time.
Date posted:
May 10, 2021
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Two companies are considering their bid strategy for installation of a computer center in a
new university. Company A is considering four alternative courses of action;
A1- bid on both the hardware and the software
A2- bid only on the hardware
A3- bid only on the software
A4- no bid.
Company B is considering three alternative courses of action:
B1- bid on both
B2- bid only on the hardware
B3- no bid.
If Company A bids a1 and Company B bids b1, then the expected payoff to Company A is
again of 2 (units of utility).
Company B is going to have a loss of 2. If company A bids a3 and Company B bids b2, then
thee expected payoff to company A is a loss of 3 (A gain of 3 to Company B). We estimate
thee payoffs in all other possible alternatives and summarize the information in the table
below.
Required:
Determine the solution of the game if:
a. Co-operation is not allowed.
b. The Company and the union can negotiate.
c. What are the limitations of a game theory in business applications.
Date posted:
May 10, 2021
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Tobil Limited produces two products namely Winfil and Bootfil. Both are components that
have a wide range of industrial applications. Tobil Limited share of the market for winfil is
insignificant but is one of a limited number of suppliers of bootfil. Winfil is a long established
product and Bootfil is a new product.
The market price off winfil is shs320 and that of Bootfil is Shs. 237.50. Tobil Limited is
unable to influence these prices.
The resource requirements for producing one unit of each of the two products are:
Materials cost Shs. 7.5 per Kg and labour costs Shs. 8 per hour. Other costs are constant.
During the coming year the company will have the following recoveries available to it; 3,000
process hours, 10,000 Kgs of material and 15,000 labour hours.
Required:
Advise the company of output combination of winfil and bootfil that will maximize its
profit in the coming year. (Support your advise with full financial analysis).
Draft a memorandum suitable for the circulation to Tobil limited board of directors
explaining the commercial limitations of the model you have used in your answer in part (a)
above.
Date posted:
May 10, 2021