Question

An automobile with a radio antenna 1.0 m long generates an emf, V1, since it is traveling at 100.0 km/h in a location where the Earth's horizontal magnetic field is 5.5x10-5T. At some time, the radio antenna doubles in length and the car begins traveling at a quarter of the original speed. What is the ratio of the new emf generated, V2, to the original emf. V1? 0.5V1 0.125 V1 111 0.75V1

Answer 1

option A

Step-by-step explanation:

given,

length of antenna = 1 m

traveling at speed = 100 Km/h

Earth's horizontal magnetic field is 5.5 x 10⁻⁵ T

radio antenna doubles in length (l₂ = 2 l)

car begins traveling at a quarter of the original speed (v₂ = v/4)

ratio of new emf

we know, ε = B l v

V₁ = B₁ l₁ v₁...........(1)

V₂ = B₂ l₂ v₂...........(2)

dividing equation (2) from (1)

`(V_2)/(V_1)=(B_2 l_2 v_2)/(B_1 l_1 v_1)`

`(V_2)/(V_1)=( (2 l)((v)/(4)))/( l v)`

`(V_2)/(V_1)=(1)/(2)`

V₂ = 0.5 V₁

the correct answer is option A