Home
Class 12
PHYSICS
Find the magnetic field at the centre O ...

Find the magnetic field at the centre O of the loop shown in the figure

Text Solution

Verified by Experts

Due to straight parts, there is no magnetic field at O. There are three fields at O
`B_(1) = (mu_(0) i)/(4pi(4R)) xx (pi)/(2) " " ( :' B = (mu_(0)i)/(4pi R) theta)`, due to arc of radius 4R
`B_(2) = (mu_(0)i)/(4pi (2R)) (pi)`, due to arc of radius 2R
`B_(3) = (mu_(0)i)/(4piR) ((pi)/(2))`, due to arc of radius R
As the current is anticlockwise in all three arcs, therefore, all the fields are prependicular to plane and outwards.
`rArr B_("net") = B_(1) + B_(2) + B_(3)`
`:. B_("net") = (mu_(0)i)/(R) [(1)/(32) + (1)/(8) + (1)/(8)]`
`= (9mu_(0)i)/(32R)`
Promotional Banner

Topper's Solved these Questions

  • MOVING CHARGES AND MAGNETISM

    AAKASH INSTITUTE ENGLISH|Exercise Illustration|14 Videos

  • MOVING CHARGES AND MAGNETISM

    AAKASH INSTITUTE ENGLISH|Exercise Try Yourself|27 Videos

  • MOVING CHARGE AND MAGNESIUM

    AAKASH INSTITUTE ENGLISH|Exercise SECTION D|16 Videos

  • NUCLEI

    AAKASH INSTITUTE ENGLISH|Exercise ASSIGNMENT (SECTION-D)|10 Videos

Similar Questions

Explore conceptually related problems

The magnetic field at the centre O of the are shown in the figure is

Find the magnetic field at the centre of the circular loop shown in figure.

The wire ABC shown in figure forms an equilateral triangle. Find the magnetic field B at the centre O of the triangle assuming the wire to be uniform.

Figure shows a square loop ABCD with edge length a. The resistance of the wire ABC is r and that of ADC is 2r. Find the magnetic field B at the centre of the loop assuming uniform wires.

Figure shows a square loop ABCD with edge length a . The resistance of the wire ABC is r and that of ADC is 2r . Find the magnetic field B at the centre of the loop assuming uniform wires.

The magnetic field at centre O of the arc in Fig.

An electric current I flows through a circular loop as shown in Figure 2(b) below. Write an expression and direction for the magnetic field at the centre of the loop at point P.

The magnetic field at the centre of the circular loop as shown in Fig. when a single wire is bent to form a circular loop and also extends to form straight sections is

A current of 2*00 A exists in a square loop of edge 10*0 cm . Find the magnetic field B at the centre of the square loop.

A wire of length 'I' is bent into a circular loop of radius R and carries a current I. The magnetic field at the centre of the loop is 'B '. The same wire is now bent into a double loop. If both loops carry the same current I and it is in the same direction, the magnetic field at the centre of the double loop will be