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Problem 1: Two wires each carrying current I are perpendicular to xy plane. The current in one of them is into the plane denoted by a cross sign and the current in the other wire is out of the plane denoted by a filled circle. If the linear distance between the positions of two wires is “2a”, then find the net magnetic field at a distance”b” on the perpendicular bisector of the line joining the positions of two wires.

Magnetic field at perpendicular bisector

Magnetic field at perpendicular bisector

Solution : The magnitudes of magnetic fields due to wires at A and B are equal. Applying Ampere's law, the magnetic field due to each wire is :

B = μ 0 I 2 π r

The magnetic fields are directed tangential to the circle drawn containing point “P” with centers “A” and “B” as shown in the figure. Each magnetic field makes an angle say “θ” with the bisector. The components in y-direction cancel out, whereas x-components add up. Clearly, the net magnetic field is directed in negative x – direction. The magnitude of net magnetic field is :

Magnetic field at perpendicular bisector

Magnetic field at perpendicular bisector

B = 2 X μ 0 I cos θ 2 π r = μ 0 I cos θ π r

Now,

cos θ = a r = a a 2 + b 2

and

r = a 2 + b 2

Putting these expressions in the equation for the magnetic field at “P”, we have :

B = μ 0 I cos θ π r = μ 0 I a π a 2 + b 2 a 2 + b 2 B = μ 0 I a π a 2 + b 2

Problem 2: Five straight wires, carrying current I, are perpendicular to the plane of drawing. Four of them are situated at the corners and fifth wire is situated at the center of a square of side "a". Two of the wires at the corners are flowing into the plane whereas the remaining three are flowing out of the plane. Find the net magnetic field at the center of square.

Five straight wires, carrying current i

Five straight wires, carrying current I

Solution : According to Ampere’s law , the magnetic field due to a straight wire carrying current "I" at a perpendicular distance "r" is given as :

B = μ 0 I 2 π R

The wires at the corners carry equal currents and the center "O" is equidistant from these wires. Thus, magnetic fields due to these four wires have equal magnitude. In order to find the directions of magnetic fields, we draw circles containing point of observation "O". The direction of magnetic field is tangential to the circle. Applying Right hand thumb rule for straight wire, we determine the orientation of magnetic field as shown in the figure. Clearly, the net magnetic field due to these four wires at the center is zero.

Directions of magnetic fields

Directions of magnetic fields

Now, magnetic field at a point on the wire itself is zero. Thus, magnetic fields due to all the five wires at the center "O" is zero.

It is interesting to note that if straight wires with currents are arranged differently, for example, two currents out of the plane at A and C respectively and the other two currents into the plane at D and E respectively are arranged, then magnetic fields do not cancel and there is net non-zero magnetic field at "O" due to currents in four wires.

Problem 3: There are five long wires perpendicular to the plane of drawing, each carrying current I as shown by filled circles (out of plane) and crosses (into the plane) in the figure below. Determine closed line integrals B . d l for each of the four contours in the direction of integration shown.

Questions & Answers

explain and give four Example hyperbolic function
Lukman Reply
The denominator of a certain fraction is 9 more than the numerator. If 6 is added to both terms of the fraction, the value of the fraction becomes 2/3. Find the original fraction. 2. The sum of the least and greatest of 3 consecutive integers is 60. What are the valu
SABAL Reply
1. x + 6 2 -------------- = _ x + 9 + 6 3 x + 6 3 ----------- x -- (cross multiply) x + 15 2 3(x + 6) = 2(x + 15) 3x + 18 = 2x + 30 (-2x from both) x + 18 = 30 (-18 from both) x = 12 Test: 12 + 6 18 2 -------------- = --- = --- 12 + 9 + 6 27 3
Pawel
2. (x) + (x + 2) = 60 2x + 2 = 60 2x = 58 x = 29 29, 30, & 31
Pawel
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Ifeanyi
on number 2 question How did you got 2x +2
Ifeanyi
combine like terms. x + x + 2 is same as 2x + 2
Pawel
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 113?
mariel Reply
Mark = x,. Don = 3x + 1 x + 3x + 1 = 113 4x = 112, x = 28 Mark = 28, Don = 85, 28 + 85 = 113
Pawel
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Harshika
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Rofiqul
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Mark
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find the value of 2x=32
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corri
X=16
Michael
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Beyan
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Mark
use the y -intercept and slope to sketch the graph of the equation y=6x
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Opoku
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4
Trista
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
Sidiki Reply
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Mark
Solve for the first variable in one of the equations, then substitute the result into the other equation. Point For: (6111,4111,−411)(6111,4111,-411) Equation Form: x=6111,y=4111,z=−411x=6111,y=4111,z=-411
Brenna
(61/11,41/11,−4/11)
Brenna
x=61/11 y=41/11 z=−4/11 x=61/11 y=41/11 z=-4/11
Brenna
Need help solving this problem (2/7)^-2
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x+2y-z=7
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-1
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how do you translate this in Algebraic Expressions
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I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
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Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
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Source:  OpenStax, Electricity and magnetism. OpenStax CNX. Oct 20, 2009 Download for free at http://cnx.org/content/col10909/1.13
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