A plane electromagnetic wave with frequency of 30 MHz travels in free space. At particular point in space and time, electric field is 6 V/m. The magnetic field at this point will be x $$\times$$ 10$$-$$8 T. The value of x is ___________.
A uniform conducting wire of length is 24a, and resistance R is wound up as a current carrying coil in the shape of an equilateral triangle of side 'a' and then in the form of a square of side 'a'. The coil is connected to a voltage source V0. The ratio of magnetic moment of the coils in case of equilateral triangle to that for square is 1 : $$\sqrt y $$ where y is ................. .
Your Input ________
Answer
Correct Answer is 3
Explanation
In triangle shape $${N_t} = {{24a} \over {3a}} = 8$$
In square $${N_s} = {{24a} \over {4a}} = 6$$
$${{{M_t}} \over {{M_3}}} = {{{N_t}I{A_t}} \over {{N_s}I{A_s}}}$$ [I will be same in both]
A coil in the shape of an equilateral triangle of side 10 cm lies in a vertical plane between the pole pieces of permanent magnet producing a horizontal magnetic field 20 mT. The torque acting on the coil when a current of 0.2 A is passed through it and its plane becomes parallel to the magnetic field will be $$\sqrt x $$ $$\times$$ 10$$-$$5 Nm. The value of x is .................
Your Input ________
Answer
Correct Answer is 3
Explanation
$$\overrightarrow \tau = \overrightarrow M \times \overrightarrow B = MB\sin 90^\circ $$
$$ = MB = {{i\sqrt 3 {l^2}} \over 4}B$$
$$ = \sqrt 3 \times {10^{ - 5}}$$ N $$-$$ m
4
JEE Main 2021 (Online) 26th August Evening Shift
Numerical
A circular coil of radius 8.0 cm and 20 turns is rotated about its vertical diameter with an angular speed of 50 rad s$$-$$1 in a uniform horizontal magnetic field of 3.0 $$\times$$ 10$$-$$2 T. The maximum emf induced the coil will be ................. $$\times$$ 10$$-$$2 volt (rounded off to the nearest integer)
Your Input ________
Answer
Correct Answer is 60
Explanation
Maximum emf $$\varepsilon = N\,\omega AB$$
N = 20, $$\omega$$ = 50, B = 3 $$\times$$ 10$$-$$2 T
