Since
${\mu}_{0}$ is exactly
$\mathrm{4\pi}\times {\text{10}}^{-7}\phantom{\rule{0.25em}{0ex}}\mathrm{T}\cdot \text{m/A}$ by definition, and because
$\text{1 T}=\text{1 N/}\left(\mathrm{A}\cdot \mathrm{m}\right)$ , the force per meter is exactly
$2\times {\text{10}}^{-7}\phantom{\rule{0.25em}{0ex}}\text{N/m}$ . This is the basis of the operational definition of the ampere.
The ampere
The official definition of the ampere is:
One ampere of current through each of two parallel conductors of infinite length, separated by one meter in empty space free of other magnetic fields, causes a force of exactly
$2\times {\text{10}}^{-7}\phantom{\rule{0.25em}{0ex}}\text{N/m}$ on each conductor.
Infinite-length straight wires are impractical and so, in practice, a current balance is constructed with coils of wire separated by a few centimeters. Force is measured to determine current. This also provides us with a method for measuring the coulomb. We measure the charge that flows for a current of one ampere in one second. That is,
$\mathrm{1\; C}=\mathrm{1\; A}\cdot \mathrm{s}$ . For both the ampere and the coulomb, the method of measuring force between conductors is the most accurate in practice.
Section summary
The force between two parallel currents
${I}_{1}$ and
${I}_{2}$ , separated by a distance
$r$ , has a magnitude per unit length given by
If you have three parallel wires in the same plane, as in
[link] , with currents in the outer two running in opposite directions, is it possible for the middle wire to be repelled by both? Attracted by both? Explain.
Suppose two long straight wires run perpendicular to one another without touching. Does one exert a net force on the other? If so, what is its direction? Does one exert a net torque on the other? If so, what is its direction? Justify your responses by using the right hand rules.
Use the right hand rules to show that the force between the two loops in
[link] is attractive if the currents are in the same direction and repulsive if they are in opposite directions. Is this consistent with like poles of the loops repelling and unlike poles of the loops attracting? Draw sketches to justify your answers.
If one of the loops in
[link] is tilted slightly relative to the other and their currents are in the same direction, what are the directions of the torques they exert on each other? Does this imply that the poles of the bar magnet-like fields they create will line up with each other if the loops are allowed to rotate?
(a) The hot and neutral wires supplying DC power to a light-rail commuter train carry 800 A and are separated by 75.0 cm. What is the magnitude and direction of the force between 50.0 m of these wires? (b) Discuss the practical consequences of this force, if any.
The force per meter between the two wires of a jumper cable being used to start a stalled car is 0.225 N/m. (a) What is the current in the wires, given they are separated by 2.00 cm? (b) Is the force attractive or repulsive?
A 2.50-m segment of wire supplying current to the motor of a submerged submarine carries 1000 A and feels a 4.00-N repulsive force from a parallel wire 5.00 cm away. What is the direction and magnitude of the current in the other wire?
The wire carrying 400 A to the motor of a commuter train feels an attractive force of
$4\text{.}\text{00}\times {\text{10}}^{-3}\phantom{\rule{0.25em}{0ex}}\text{N/m}$ due to a parallel wire carrying 5.00 A to a headlight. (a) How far apart are the wires? (b) Are the currents in the same direction?
An AC appliance cord has its hot and neutral wires separated by 3.00 mm and carries a 5.00-A current. (a) What is the average force per meter between the wires in the cord? (b) What is the maximum force per meter between the wires? (c) Are the forces attractive or repulsive? (d) Do appliance cords need any special design features to compensate for these forces?
Find the direction and magnitude of the force that each wire experiences in
[link] (a) by, using vector addition.
(a) Top wire:
$2\text{.}\text{65}\times {\text{10}}^{-4}\phantom{\rule{0.25em}{0ex}}\text{N/m}$ s,
$\text{10}\text{.}\mathrm{9\xba}$ to left of up
(b) Lower left wire:
$3\text{.}\text{61}\times {\text{10}}^{-4}\phantom{\rule{0.25em}{0ex}}\text{N/m}$ ,
$\text{13}\text{.}\mathrm{9\xba}$ down from right
(c) Lower right wire:
$3\text{.}\text{46}\times {\text{10}}^{-4}\phantom{\rule{0.25em}{0ex}}\text{N/m}$ ,
$\text{30}\text{.}\mathrm{0\xba}$ down from left
A petrol engine has a output of 20 kilowatts and uses 4.5 kg of fuel for each hour of running. The energy given out when 1 kg of petrol is burnt is 4.8 × 10 to the power of 7 Joules.
a) What is the energy output of the engine every hour?
b) What is the energy input of the engine every hour?
A simple pendulum is used in a physics laboratory experiment to obtain an experimental value for the gravitational acceleration, g . A student measures the length of the pendulum to be 0.510 meters, displaces it 10 o from the equilibrium position, and releases it. Using a s
Two masses of 2 kg and 4 kg are held with a compressed spring between them. If the masses are released, the spring will push them away from each other. If the smaller mass moves off with a velocity of 6m/s, what is the stored energy in the spring when it is compressed?
Reduce that two body problem into one body problem. Apply potential and k. E formula to get total energy of the system
rakesh
i dont think dere is any potential energy... by d virtue of no height present
Olalekan
there is compressed energy,dats only potential energy na?
rakesh
yes.. but... how will u approach that question without The Height in the question?
Olalekan
Can you explain how you get 54J?
Emmanuel
Because mine is 36J
Emmanuel
got 36J too
Douglas
OK the answer is 54J
Babar is correct
Emmanuel
Conservation of Momentum
Emmanuel
woow i see.. can you give the formula for this
joshua
Two masses of 2 kg and 4 kg are held with a compressed spring between them. If the masses are released, the spring will push them away from each other. If the smaller mass moves off with a velocity of 6m/s, what is the stored energy in the spring when it is compressed? Asume there is no external force.
may be by using MC^2=MC^2 and Total energy=kinetic energy +potential energy
so 1st find kinetic energy and den find potential energy which is stored energy
we are given f=12 m=200g which is 0.2kg
now from 2nd law of newton a= f/m=60m/s*2
work done=force applied x displacement cos (theta)
w= 12x60 =720nm/s*2
Mudang
this very interesting question very complicated for me, í need urgent help.
1,two buses A and B travel along the same road in the same direction from Harper city (asume They both started from the same point) to Monrovia. if bus A maintains a Speedy of 60km/h and bus B a Speedy of 75km/h, how many
mohammed
hours Will it take bus B to overtake bus A assuming bus B starts One hour after bus A started. what is the distance travelled by the buses when They meet?.
mohammed
pls í need help
mohammed
4000 work is done
Ana
speed=distance /time
distance=speed/time
Ana
now use this formula
Ana
what's the answer then
Julius
great Mudang
Kossi
please Ana
explain 4000 ?
babar
hey mudang
there is a product of force and acceleration not force and displacement
babar
@Mohammed answer is 0.8hours or 48mins
Douglas
nice
A.d
its not possible
Olalekan
í want the working procedure
mohammed
the answer is given but how Will One arrive at it. the answers are 4hours and 300m.
mohammed
physics is the science that studies the non living nature
For first equation simply integrate formula of acceleration in the limit v and u
Tripti
For second itegrate velocity formula by ising first equation
Tripti
similarly for 3 one integrate acceleration again by multiplying and dividing term ds
Tripti
any methods can take to solve this eqtions
a=vf-vi/t
vf-vi=at
vf=vi+at......1
Ana
suppose a body starts with an initial velocity vi and travels with uniform acceleration a for a period of time t.the distance covered by a body in this time is "s" and its final velocity becomes vf
Ana
what is the question dear
Zeeshan
average velocity=(vi+vf)/2
distance travelled=average velocity ×time
therefore s=vi+vf/2×t
from the first equation of motion ,we have
vf =vi+at
s=[vi+(vi+at)]/2×t
s=(2vi+at)/2×t
s=bit+1/2at2
Ana
find the distance
Ana
how
Zeeshan
Two speakers are arranged so that sound waves with the same frequency are produced and radiated through a room. An interference pattern is created. Calculate the distance between the two speakers?