Home
Class 12
PHYSICS
A copper wire has a square cross section...

A copper wire has a square cross section of 6 mm on a side. The wire is 10 m long and carries a current of 3.6A. The density of free electrons id `8.5x10^(28)//m^3.`Find the magnitude of (a) the current density in the wire , (b) the electric field in the wire. (c ) How much time is required for an electron to travel the length of the wire? `("rh, electrical resistivity, is" 1.72 xx10^(-8) Omegam.)`

Text Solution

Verified by Experts

Given ` r= 6 mm, I = 10 m, I = 3.6 A, n = 8.5xx10^(28)//m^3`
(a) To find the currrent density, formula used should be
`J=I//A =(3.6)/((6xx10^(-3))^(2))=(3.6)/(36xx10^(-6))=10^(5) Am^(-2)`
(b) Electric field is
`E = rhoJ = 1.72xx10^(-8) xx10^5 = 1.72 xx10^(-3)Vm^(-1)`
(c ) Time taken is
`t = (I)/(v_d) = (I"ne"A)/(I)`
`=(10xx8.5xx10^(28)xx1.6xx10^(-19)xx(6xx10^(-3))^(2))/(3.6)`
`=1.36xx10^6 s`
Promotional Banner

Topper's Solved these Questions

  • ELECTRIC CURRENT AND CIRCUIT

    CENGAGE PHYSICS ENGLISH|Exercise Solved Examples|12 Videos

  • ELECTRIC CURRENT AND CIRCUIT

    CENGAGE PHYSICS ENGLISH|Exercise Exercise 5.1|28 Videos

  • ELECTRIC CURRENT & CIRCUITS

    CENGAGE PHYSICS ENGLISH|Exercise Kirchhoff s law and simple circuits|15 Videos

  • ELECTRIC FLUX AND GAUSS LAW

    CENGAGE PHYSICS ENGLISH|Exercise MCQ s|38 Videos

Similar Questions

Explore conceptually related problems

A copper wire has a square cross-section, 2.0 mm on a side. It carries a current of 8 A and the density of free electrons is 8 xx 10^(28)m^(-3) . The drift speed of electrons is equal to

The current density in a wire is 10A//cm^(2) and the electric field in the wire is 5 V/cm. If p = resistivity of material, sigma = conductivity of the material then (in SI unit)

A 150 m long metal wire connects points A and B. The electric potential at point B is 50V less than that at point A. If the conductivity of the metal is 60 xx 10^(6)mho//m then magnitude of the current density in the wire is equal to:

An aluminium wire carrying a current has diameter 0.84 mm . The electric field in the wire 0.49 V//m . What is (a) the current carried by the wire? (b) the potential difference between two points in the wire 12.0 m apart? (c) the resistance of a 12.0 m length of this wire? Specific resistance of aluminium is 2.75 xx 10^-8 Omega -m.

A uniform copper wire having a cross sectional area of 1 mm^(2) carries a current of 5 A. Calculate the drift speed of free electrons in it. (Free electron number of density of copper =2 times 10^(28)//m^(3) .)

A current of 1.8 A flows through a wire of cross-sectional area 0.5 mm^(2) ? Find the current density in the wire. If the number density of conduction electrons in the wire is 8.8 xx 10^(28) m^(-3) , find the drift speed of electrons.

A straight wire carries a current of 10A. An electron moving at 10^(3) m/s is at distance 2.0 cm from the wire. Find the force acting on the electron if its velocity is directed toward the wire?

A copper wire having cross- sectional area of 0.5 mm^2 and a length of 0.1 m is initially at 25^@C and is thermally insulated form the surrounding. If a current of 10A is set up in this wire, (a) find the time in which the wire will start melting. (b) What will be the change of resistance with time, if the length of the wire is doubled? For copper, resistivity is 1.6xx10^(-8)Omega m, density is 9,000 kgm^(-3) and specific heat capacity is 0.09 cal g^(-1)C^(-1). Melting temperature of copper is 1075^@C

A long, cylindrical wire of radius b carries a current i distributed uniformly over its cross section. Find the magnitude of the magnetic field at a point inside the wire at a distance a from the axis.

A straight copper-wire of length 100m and cross-sectional area 1.0mm^(2) carries a current 4.5A . Assuming that one free electron corresponds to each copper atom, find (a) The time it takes an electron to displace from one end of the wire to the other. (b) The sum of electrostatic forces acting on all free electrons in the given wire. Given resistivity of copper is 1.72xx10^(-8)Omega-m and density of copper is 8.96g//cm^(3) .