Advertisements
Advertisements
प्रश्न
Five long wires A, B, C, D and E, each carrying current I are arranged to form edges of a pentagonal prism as shown in figure. Each carries current out of the plane of paper.
- What will be magnetic induction at a point on the axis O? AxisE is at a distance R from each wire.
- What will be the field if current in one of the wires (say A) is switched off?
- What if current in one of the wire (say) A is reversed?
Advertisements
उत्तर
a. The wires shown in this problem carrying current outwards to the plane. And we know that direction of magnetic field is perpendicular to both current and position vector r. So, the vector sum of magnetic field produced by each wire at O is equal to 0.
Suppose the five wires A, B, C, D and E be perpendicular to the plane of paper at locations as shown in figure.
Thus, magnetic field induction due to five wires will be represented by various sides of closed pentagon in one order, lying in the plane of paper. So, its value is zero.
b. When current in AA' is switched off, then B1 = 0 and resultant becomes
R = B2 + B3 + B4 + B5
But form (a) part B1 + B2 + B3 + B4 + B5 = 0
Or `vecB_2 + vecB_3 + vecB_4 + vecB_5 = - vecB_1`
R = – B1
R = `(mu_0I)/(2pir)`
i.e. Direction of resultant is opposite to `vecB_1`.
c. If current in wire A is reversed, then
Total magnetic field induction at O = Magnetic field induction due to A + Magnetic field induction due to wires B, C, D and E
= `(mu_0)/(4piR) (2I)/R` (acting perpendicular to AO towards left) + `(mu_0)/pi (2I)/R` (acting perpendicular AO towards left)
= `(mu_0I)/(piR)` acting perpendicular AO towards left.
APPEARS IN
संबंधित प्रश्न
How does one understand this motional emf by invoking the Lorentz force acting on the free charge carriers of the conductor? Explain.
Two long and parallel straight wires A and B carrying currents of 8.0 A and 5.0 A in the same direction are separated by a distance of 4.0 cm. Estimate the force on a 10 cm section of wire A.
Two long straight parallel conductors 'a' and 'b', carrying steady currents Ia and Ib are separated by a distance d. Write the magnitude and direction of the magnetic field produced by the conductor 'a' at the points along the conductor 'b'. If the currents are flowing in the same direction, what is the nature and magnitude of the force between the two conductors?
A long, straight wire of radius R carries a current distributed uniformly over its cross section. T he magnitude of the magnetic field is
(a) maximum at the axis of the wire
(b) minimum at the axis of the wire
(c) maximum at the surface of the wire
(d) minimum at the surface of the wire.
A copper wire of diameter 1.6 mm carries a current of 20 A. Find the maximum magnitude of the magnetic field `vecB` due to this current.
A long, straight wire of radius r carries a current i and is placed horizontally in a uniform magnetic field B pointing vertically upward. The current is uniformly distributed over its cross section. (a) At what points will the resultant magnetic field have maximum magnitude? What will be the maximum magnitude? (b) What will be the minimum magnitude of the resultant magnetic field?
A hypothetical magnetic field existing in a region is given by `vecB = B_0 vece` where `vece`_r denotes the unit vector along the radial direction. A circular loop of radius a, carrying a current i, is placed with its plane parallel to the x−y plane and the centre at (0, 0, d). Find the magnitude of the magnetic force acting on the loop.
The magnetic field existing in a region is given by `vecB = B_0(1 + x/1)veck` . A square loop of edge l and carrying a current i, is placed with its edges parallel to the x−y axes. Find the magnitude of the net magnetic force experienced by the loop.
Four long, straight wires, each carrying a current of 5.0 A, are placed in a plane as shown in figure. The points of intersection form a square of side 5.0 cm.
(a) Find the magnetic field at the centre P of the square.
(b) Q1, Q2, Q3, and Q4, are points situated on the diagonals of the square and at a distance from P that is equal to the diagonal of the square. Find the magnetic fields at these points.
A straight, how wire carries a current of 20 A. Another wire carrying equal current is placed parallel to it. If the force acting on a length of 10 cm of the second wire is 2.0 × 10−5 N, what is the separation between them?
Two parallel wires separated by a distance of 10 cm carry currents of 10 A and 40 A along the same direction. Where should a third current by placed so that it experiences no magnetic force?
A conducting circular loop of radius a is connected to two long, straight wires. The straight wires carry a current i as shown in figure. Find the magnetic field B at the centre of the loop.
Answer the following question.
Two infinitely long straight wire A1 and A2 carrying currents I and 2I flowing in the same direction are kept' distance apart. Where should a third straight wire A3 carrying current 1.5 I be placed between A1 and A2 so that it experiences no net force due to A1 and A2? Does the net force acting on A3 depend on the current flowing through it?
Three infinitely long parallel straight current-carrying wires A, B and C are kept at equal distance from each other as shown in the figure. The wire C experiences net force F. The net force on wire C, when the current in wire A is reversed will be ______.
Do magnetic forces obey Newton’s third law. Verify for two current elements dl1 = dlî located at the origin and dl2 = dlĵ located at (0, R, 0). Both carry current I.
Two long straight parallel conductors carrying currents I1 and I2 are separated by a distance d. If the currents are flowing in the same direction, show how the magnetic field produced by one exerts an attractive force on the other. Obtain the expression for this force and hence define 1 ampere.
Two long parallel wires kept 2 m apart carry 3A current each, in the same direction. The force per unit length on one wire due to the other is ______.
