Question

A narrow copper wire of length L and radius b is attached to a wide copper wire of length L and radius 2b, forming one long wire of length 2L. This long wire is attached to a battery, and a current is flowing through it. If the electric field in the narrow wire is E, the electric firld in the wide wire is.a. Eb. E/4 c. 4E d. E/2 e. 2E

Answer 1

Answer:

E.

Explanation:

As we know that Current in both wire  will be same but both have different resistance as per

$R_1 = \rho L/A$

$R_2 =\rho L/4A$ (As the radius is doubled so cross sectional area will become four times).

Hence,  $R_1 = 4\times(R_2)$

therefore,  if current is same in both then voltage will be -

$V_1=4\times(V_2)$ (As V proportional to R , i is same in all)

then-

$E_1 = 4(E_2)$ (As E proportional V , r is same in all)

$\Rightarrow E2 = \frac{(E_1)}{4}$(Electric feild in wide wire)

Option E.