Question

B_x and B_y are the magnetic fields at the centre of two coils X and Y respectively each carrying equal current. If coil X has 200 turns and 20 cm radius and coil Y has 400 turns and 20 cm radius, the ratio of B_x and B_y is ______.

Options

• 1:1

• 1:2

• 2:1

• 4:1

Answer 1

B_x and B_y are the magnetic fields at the centre of two coils X and Y respectively each carrying equal current. If coil X has 200 turns and 20 cm radius and coil Y has 400 turns and 20 cm radius, the ratio of B_x and B_y is 1:2.

Explanation:

The magnetic field at the centre of coil, B

= `(mu_0"Ni")/(2"R")`

Given, for coil x

Number of turns, N_x = 200

Radius, R_x = 20 cm

⇒ B_x = `(mu_0"N"_x"i")/(2"R"_x)=(200mu_0"i")/(2xx20)`    ...(i)

For coil y 

Number of turns, N_y = 400

Radius, R_y = 20 cm

 ⇒ B_y = `(mu_0"N"_"y""i")/(2"R"_"y")=(400mu_0"i")/(2xx20)`    ...(ii) 

Divide equation (i) by equation (ii), we have

 ⇒ `"B"_x/"B"_"y"=((200mu_0"i")/(2xx20))/((400mu_0"i")/(2xx20)`

= `1/2`