# Force on a Finite Wire

## Trending Questions

**Q.**

Dimensional formula for inductance

**Q.**A current carrying closed loop, in the form of a right-angled isosceles triangle ABC, is placed in a uniform magnetic field directed alongside AB. If the magnetic force on the arm BC is F, the force on the arm AC is

- −F
- F
- F√2
- −F√2

**Q.**An arrangement of three parallel straight wires placed perpendicular to plane of paper carrying same current i along the same direction is shown in fig. Magnitude of force per unit length on the middle wire 'B' is given by

- μ0i2√2πd
- μ0i22πd
- 2μ0i2πd
- √2μ0i2πd

**Q.**The variation of electric field between two charges q1 and q2 along the line joining the charges is plotted against the distance r from q1 (taking the direction from q1 to q2 as positive) as shown in the figure. Find the correct statement among the following is

- q1 and q2 are positive and |q1|<|q2|
- q1 and q2 are positive and |q1|>|q2|
- q1 is positive and q2 is negative |q1|<|q2|
- q1 and q2 are negative and |q1|<|q2|

**Q.**A closed loop PQRS carrying a current is placed in a uniform magnetic field. If the magnetic forces on segments PS, SR and RS are F1, F2 and F3 respectively and are in the plane of the paper and along the directions shown, the force on the segment QP is

- F3−F1+F2
- F3−F1−F2
- √(F3−F1)2+F22
- √(F3−F1)2−F22

**Q.**A vertical wire carrying a current in the upward direction is placed in a horizontal magnetic field directed towards north. The wire will experience a force directed towards

- North
- West
- South
- East

**Q.**A wire carrying a current i is kept in X-Y plane along the curve Y=A sin(2πλx). A magnetic field B exists in the Z-direction as shown. Find the magnitude of the magnetic force on the portion of the wire between x=0 and x=λ

- Zero
- iλB

- iλB2

- 32iλB

**Q.**A square of side of 2.0 m is placed in a uniform magnetic field →B=2.0 T in a direction perpendicular to the plane of the square inwards. Equal current i=3.0 A is flowing in the directions shown in figure. Find the magnitude of magnetic force acting on the loop ABCD.

- 18√2 N
- 27√2 N
- 36√2 N
- 16√2 N

**Q.**3 A of current is flowing in a linear conductor having a length of 40 cm. The conductor is placed in a magnetic field of strength 500 gauss and makes an angle of 30∘ with the direction of the field. It experiences a force of magnitude

- 3×104 N.
- 3×102 N.
- 3×10−2 N.
- 3×10−4 N.

**Q.**Consider the situation shown in figure. If the lines are drawn in proportion to the charge, what is the ratio |q1||q2| ?

- 1:2
- 2:1
- 3:1
- 1:3

**Q.**A conducting rod of length l and mass m is moving down a smooth inclined plane of inclination θ with constant velocity v. A current I is flowing in the conductor in a direction perpendicular to the paper inwards. A vertically upward magnetic field →B exists in space. Then, magnitude of magnetic field →B is

- mgIlsin θ
- mgIltan θ
- mg cosθIl
- mgIl sin θ

**Q.**Same current I=2 A is flowing in a wire frame as shown in the figure. The frame is combination of two equilateral triangles ACD and CDE of side 1 m. It is placed in a uniform magnetic field B=4 T acting perpendicular to the plane of frame. The magnitude of magnetic force acting on the frame is

- 24 N
- Zero
- 16 N
- 8 N

**Q.**

A wire carrying a current i is placed in a uniform magnetic field in the form of the curve y=a sin(πxL)0≤x≤2L. The force acting on the wire is

Zero

**Q.**A straight conducting rod of length 30 cm and having a resistance of 0.2 Ω is allowed to slide over two parallel thick metallic rails with uniform velocity of 0.2 ms−1 as shown in the figure. The rails are stacked in a horizontal plane. If the horizontal component of earth's magnetic field is 0.3×10−4 T and a steady current of 3μA is induced through the rod. The angle of dip will be

- tan−1(13)
- tan−1(√3)
- tan−1(1√3)
- tan−1(34)

**Q.**A uniform magnetic field →B=Bo^k exists in a region . A current carrying wire is placed in x−y plane as shown in the figure. The magnetic force acting on the part AB of wire is:

- 2Boia ^i
- −3Boia ^j
- −3Boia ^k
- −Boia ^j

**Q.**Find electric field due to finite line charge at point P.

- 55 N/C
- 65 N/C
- 75 N/C
- 85 N/C

**Q.**A current carrying wire LN is bent in the from shown below. If wire carries a current of 10A and it is placed in a magnetic field of 5T which acts perpendicular to the paper outwards then it will experience a force

- 5 N
- Zero
- 20 N
- 30 N

**Q.**

Draw a labelled diagram of Van de Graaff generator. State its working principle to show how introducing a small charged sphere into a larger sphere, a large amount of charge can be transferred to the outer sphere. State the use of this machine and also point out its limitations.

**Q.**The electric field E is measured at a point P(0, 0, d) generated due to various charge distributions and the dependence of E on d is found to be different for different charge distributions.

Column-II describes different electric charge distributions, along with their locations. Match the functions in column-I with the related charge distributions in column-II.

column -I | column-II |

(A) E is independent of d | (P) A point charge Q at the origin |

(B) E∝1d | (Q) A small dipole with point charges Q at (0, 0, l) and −Q at (0, 0, −l). Take 2l<<<d. |

(C) E∝1d2 | (R) An infinite line charge coincident with the x- axis, with uniform linear charge density λ |

(D) E∝1d3 | (S) Two infinite wire carrying uniform linear charge density parallel to the x-axis. The one along (y=0, z=l) has a charge density λ and the another along (y=0, z=−l) has a charge density −λ. Take 2l<<d. |

(T) Infinite plane charge coincident with the xy-plane with uniform surface charge density. |

Which of the following option has the correct combiantion considering coulumn-I and column-II.

- A→T
- B→S
- C→Q, R
- D→T

**Q.**A conducting rod PQ of length l=1.0 m is moving with a uniform speed v=2 m/s in a uniform magnetic field B=4.0 T directed into the paper. A capacitor of capacity C=10 μF is connected as shown in the figure. Then charge on plate A(in μC) is

**Q.**

A rectangular loop ABCD, carrying a current 15 A, is placed near a long wire carrying a current 40 A. The resultant force acting on the loop is

6.4×10−2 N directed away from wire

6.4×10−2 N directed towards wire

3.6×10−2 N directed away from wire

3.6×10−2 N directed towards the wire

**Q.**A metal strip 6.50 cm long, 0.85 cm wide moves with constant velocity →v through a uniform magnetic field B=1.20 mT, directed perpendicular to the strip, as shown in the figure. A potential difference of 3.90 μV is measured between points x and y across the strip. Calculate the speed v.

- 2.5 m/s
- 5.5 m/s
- 1.4 m/s
- 0.4 m/s

**Q.**

A wire of mass m and length l can slide freely on a pair of smooth, vertical rails (figure 38-E31). A magnetic field B exists in the region in the direction perpendicular to the plane of the rails. The rails are connected at the top end by a capacitor of capacitance C. Find the acceleration of the wire neglecting any electric resistance.

**Q.**A rod has a total charge Q, uniformly distributed along its length L. If the rod rotates with angular velocity ω about its end, compute its magnetic moment.

- QωL22
- QωL26
- QωL23
- QωL24

**Q.**A wire bent as shown in figure carries a current i and is placed in a uniform field of magnetic induction →B that emerges out from the plane of the figure.The magnetic force acting on the wire is:

- 2BIR
- 4BIR
- BIR
- 52BIR

**Q.**A metal rod of mass 10 gm and length 25 cm is suspended on two springs as shown in figure. The springs are extended by 4 cm. When a 20 ampere current passes through the rod it rises by 1 cm. Determine the magnetic field assuming acceleration due to gravity be 10 m/s2.

- 5 T
- 10 T
- 0.5×10−2 T
- 5×10−2 T

**Q.**

A steamboat goes across a lake and comes back

$\left(a\right)$ On a quiet day when the water is still and

$\left(b\right)$ On a rough day when there is a uniform air current so as to help the journey onward and to impede the journey back.

If the speed of the launch on both days was the same, in which case it will complete the journey in lesser time

Case $\left(a\right)$

Case $\left(b\right)$

Same in both

Nothing can be predicted

**Q.**

A magnetic needle is placed in a uniform magnetic field and is aligned with the field. The needle is now rotated by an angle of 60∘ and the work is W. The torque on the magnetic needle at this position is:

√3W

2√3W

√32W

**Q.**

Two long parallel wires carrying currents 2.5 A and "I" A in the same direction (directed in the o plane) are held at P and Q respectively as shown. The points P and Q are located at a distance of 5 m and 2 m respectively from a collinear point R. An electron moving with a velocity of 4×105 ms−1 along the positive x-axis experiences a force of magnitude 3.2×10−20 N at the point R. The value of I is

4 A

8 A

6 A

2 A

**Q.**In the figure shown, the magnitude of magnetic force on the wire ABC in the given uniform magnetic field will be:

(B=2 Tesla)

- 4(3+2π) N
- 20 N
- 30 N
- 40 N