A square loop of ABCD carrying a current i, is placed near and coplanar with a long straight conductor XY carrying a current I, the net force on the loop will be

$fraction numerator straight mu subscript straight o li over denominator 2 straight pi end fraction$
$fraction numerator 2 straight mu subscript straight o liL over denominator 3 straight pi end fraction$
$fraction numerator straight mu subscript straight o liL over denominator 2 straight pi end fraction$
$fraction numerator 2 straight mu subscript straight o li over denominator 3 straight pi end fraction$

Solution

fraction numerator 2 straight mu subscript straight o li over denominator 3 straight pi end fraction

In the above fig., the direction of currents in a long straight conductor XY and arm AB of a square loop ABCD are in the same direction.
So, there exists a force of attraction between the two conductors, which will be experienced by F_AB as,
$straight F subscript BA space equals space fraction numerator straight mu subscript straight o space straight I space straight i space straight L over denominator 2 straight pi space open parentheses begin display style straight L over 2 end style close parentheses end fraction$
In the case of XY and arm CD, the direction of currents are in the opposite direction.
There exists a force of repulsion which will be experience by CD as,
$straight F subscript CD equals space fraction numerator straight mu subscript straight o IiL over denominator 2 straight pi open parentheses begin display style fraction numerator 3 straight L over denominator 2 end fraction end style close parentheses end fraction$
Therefore, net force on the loop ABCD is,
F_loop = F_BA - F_CD = $fraction numerator straight mu subscript straight o IiL over denominator 2 straight pi end fraction open parentheses fraction numerator 1 over denominator left parenthesis L divided by 2 right parenthesis end fraction minus fraction numerator 1 over denominator left parenthesis 3 L divided by 2 right parenthesis end fraction close parentheses$
F_loop = $fraction numerator 2 straight mu subscript straight o iI over denominator 3 straight pi end fraction$

Some More Questions From Current Electricity Chapter

What conclusion can you draw from the following observations on a resistor made of alloy manganin?

Current A

Voltage V

Current A

Voltage V

0.2

0.4

0.6

0.8

1.0

2.0

3.94

7.87

11.8

15.7

19.7

39.4

3.0

4.0

5.0

6.0

7.0

8.0

59.2

78.8

98.6

118.5

138.2

158.0

Answer the following questions:
A steady current flows in a metallic conductor of non-uniform cross-section. Which of these quantities is constant along the conductor: current, current density, electric field, drift speed?

Answer the following questions:
Is Ohm’s law universally applicable for all conducting elements? If not, give examples of elements which do not obey Ohm’s law.

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Current Electricity

Some More Questions From Current Electricity Chapter

What conclusion can you draw from the following observations on a resistor made of alloy manganin?

Current A

Voltage V

Current A

Voltage V

0.2

0.4

0.6

0.8

1.0

2.0

3.94

7.87

11.8

15.7

19.7

39.4

3.0

4.0

5.0

6.0

7.0

8.0

59.2

78.8

98.6

118.5

138.2

158.0

Answer the following questions:
A steady current flows in a metallic conductor of non-uniform cross-section. Which of these quantities is constant along the conductor: current, current density, electric field, drift speed?

Answer the following questions:
Is Ohm’s law universally applicable for all conducting elements? If not, give examples of elements which do not obey Ohm’s law.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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Email Address

Location

For Daily Free Study Material Join wiredfaculty

Current Electricity

A square loop of ABCD carrying a current i, is placed near and coplanar with a long straight conductor XY carrying a current I, the net force on the loop will be

Some More Questions From Current Electricity Chapter

What conclusion can you draw from the following observations on a resistor made of alloy manganin? Current A Voltage V Current A Voltage V 0.2 0.4 0.6 0.8 1.0 2.0 3.94 7.87 11.8 15.7 19.7 39.4 3.0 4.0 5.0 6.0 7.0 8.0 59.2 78.8 98.6 118.5 138.2 158.0

Answer the following questions:A steady current flows in a metallic conductor of non-uniform cross-section. Which of these quantities is constant along the conductor: current, current density, electric field, drift speed?

Answer the following questions:Is Ohm’s law universally applicable for all conducting elements? If not, give examples of elements which do not obey Ohm’s law.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

What conclusion can you draw from the following observations on a resistor made of alloy manganin?

Current A

Voltage V

Current A

Voltage V

0.2

0.4

0.6

0.8

1.0

2.0

3.94

7.87

11.8

15.7

19.7

39.4

3.0

4.0

5.0

6.0

7.0

8.0

59.2

78.8

98.6

118.5

138.2

158.0

Answer the following questions:
A steady current flows in a metallic conductor of non-uniform cross-section. Which of these quantities is constant along the conductor: current, current density, electric field, drift speed?

Answer the following questions:
Is Ohm’s law universally applicable for all conducting elements? If not, give examples of elements which do not obey Ohm’s law.