Chapter 21, Problem 16P

To determine

The magnetic field.

Answer to Problem 16P

Solution:

Magnetic field is $\text{1}\text{.126 T}$

Explanation of Solution

Given info:

External force $\left(F\right)\text{ = 0}\text{.350 N}$

Resistance $\left(R\right)\text{ = 0}\text{.25 Ω}$

Length $\left(l\right)\text{= 20}\text{.0 cm }$

$\text{ = 0}\text{.200 m}$

Speed $\left(v\right)\text{= 1}\text{.50 }m/s$

The relation between the external force to the magnetic field is given by

Formula to be used:

$F_E\text{= }\frac{B^{\text{2}}{l}^{\text{2}}v}{R}$

Calculation:

Here, two forces are equal and opposite, net force is zero so net acceleration is also zero. Then, the rod moves with constant speed.

Applying values,

$0.305=\frac{\left(B^2\right)\times {\left(0.200\right)}^2\times 1.5}{0.25}$

$\begin{array}{l}\Rightarrow B^{\text{2}}\text{=1}\text{.270}\\ B\text{=1}\text{.126 T}\end{array}$