Advertisements
Advertisements
Question
Two identical circular coils, P and Q each of radius R, carrying currents 1 A and √3A respectively, are placed concentrically and perpendicular to each other lying in the XY and YZ planes. Find the magnitude and direction of the net magnetic field at the centre of the coils.
Advertisements
Solution
Magentic field at the centre of the coil are perpendicular to each other. Therefore net magnetic field (B) is the resultant of the two fields caused due to coil P and Q, respectively.
`B_P = (μ_oI)/(2πR)= (μ_o)/(2πR)`
`B_Q= (μ_oI)/(2πR)= (μ_osqrt3)/(2πR)`
Net magnetic field, `B = sqrt(B_P^2 + B_Q^2)`
`=sqrt((μ_o/(2πR))^2 + ( (μ_osqrt3)/(2πR))^2) `
`= μ_o/(2πR)sqrt4`
`= μ_o/(πR)`
For direction of net magnetic field
`tanβ =(AB)/(BC)`
`= (μ_o/(2πR))/((μ_osqrt3)/(2πR)) = 1/sqrt3`
`β= 30^@`
The direction of net magnetic field is 30° with the X-direction.
RELATED QUESTIONS
Use Biot-Savart law to derive the expression for the magnetic field on the axis of a current carrying circular loop of radius R.
Draw the magnetic field lines due to a circular wire carrying current I.
Two concentric circular coils X and Y of radii 16 cm and 10 cm, respectively, lie in the same vertical plane containing the north to south direction. Coil X has 20 turns and carries a current of 16 A; coil Y has 25 turns and carries a current of 18 A. The sense of the current in X is anticlockwise, and clockwise in Y, for an observer looking at the coils facing west. Give the magnitude and direction of the net magnetic field due to the coils at their centre.
At a place, the horizontal component of earth's magnetic field is B and angle of dip is 60°. What is the value of horizontal component of the earth's magnetic field at equator?
Using Biot-Savart law, deduce the expression for the magnetic field at a point (x) on the axis of a circular current carrying loop of radius R. How is the direction of the magnetic field determined at this point?
Use Biot-Savart's law to find the expression for the magnetic field due to a circular loop of radius 'r' carrying current 'I', at its centre ?
A circular loop of radius 20 cm carries a current of 10 A. An electron crosses the plane of the loop with a speed of 2.0 × 106 m s−1. The direction of motion makes an angle of 30° with the axis of the circle and passes through its centre. Find the magnitude of the magnetic force on the electron at the instant it crosses the plane.
A circular loop of radius r carries a current i. How should a long, straight wire carrying a current 4i be placed in the plane of the circle so that the magnetic field at the centre becomes zero?
A circular loop of radius 4.0 cm is placed in a horizontal plane and carries an electric current of 5.0 A in the clockwise direction as seen from above. Find the magnetic field (a) at a point 3.0 cm above the centre of the loop (b) at a point 3.0 cm below the centre of the loop.
The magnitude of the magnetic field due to a circular coil of radius R carrying a current I at an axial distance x from the centre is ______.
A charged particle moving in a uniform magnetic field and losses 4% of its kinetic energy. The radius of curvature of its path changes by ______.
