A garden is to be laid out in a rectangular area and protected by wire fence. What is the largest possible area of the fenced garden with 40 metres of wire.

A garden is to be formed in a rectangular shape and projected by wire fence. What is the largest possible area of the fenced garden with 60 metres of wire.

A wire of length 28 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a circle. What should be the length of the two pieces so that the combined area of the square and the circle is minimum?

A running track of 440 ft is to be laid out enclosing a football field, the shape of which is a rectangle with a semi-circle at each end. If the area of the rectangular portion is to be maximum, then find the length of its sides.

Two wire A & B are of the same metal and are of same length have area of cross section in the ratio of 2:1 If the same potential difference is applied across each wire. What will be the ratio of the current flowing through the wires A & B ?

A circular coil of 20 hours and radius 10cm is placed in an uniform magnetic field of 0.17 normal to the plane of the coil if the current in the coil is 5.0A . What is the average force on each electron in the coil due to the magnetic field ? The coil is made of copper wire of cross - (a) sectional area 10^(-5) m ^(+2) and the free clectron density in copper is given to be about 10^(29)//m^(3) .

A garden measuring 12m by 16m is to have wide installed all the way around so that it incease the total area of 285m^(2) . What is the width of the pathway?

A currrent I is passed through a silver strip of width d and area of cross section A. The number of free electrons per unit volume is n. (a) Find the drift velocity v of the electrons. (b) If a magnetic field B exists in the region as shown in what is the average magnetic force on the free electrons? (c) Due to the magnetic force, the free electrons get accumulated on one side of the conductor along its length. This produces a transverse electric field in the conductor which opposes the magnetic force on the electrons. Find the magnitude of the electric field which will be the potential diference developed across the width of the conductor due to the electron- accumulation? The appearance of a transverse emf, when a current-carrying wire is placed in a magnetic field, is called hall effect.

a. The top of the atmosphere is at about 400 kV with respectto the surface of the earth, corresponding to an electric field that decreases with altitude. Near the surface of the earth, the field is about 100 Vm^(-1). Why then do we not get a electric shock as we step out of our house into the openy (Assume the house to be a steel cage so there is no field inside!) b. A man fixes outside his house one evening a two metre high insulating slab carrying on its top a large aluminium sheet of area 1m^(2) . Will he get an electric shock if he touches the metal sheet next morning? c. The discharging current in the atmosphere due to the small conductivity of air is known to be 1800A on an average over the globe. Why then does the atmosphere not discharge itself completely in due course and become electrically neutral? In other words, what keeps the atmosphere charged? d. What are the forms of energy into which the electrical energy of the atmosphere is dissipated during a lightning? (Hint: The earth has an electric field of about 100 Vm^(-1) at its surface in the downward direction, corresponding to a surface charge density =-10^(-9) Cm^(-2) ?.

A steel wire of length 2.0 m is stretched through 2.0 mm. The cross sectional area of the wire is 4.0 mm^2. Calculate the elastic potential energy stored in the wire in the stretched condition. Young modulus of steel =2.0x10^11Nm^-2