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A uniform magnetic field of $1.5 \mathrm{~T}$ exists in a cylindrical region of radius $10.0 \mathrm{~cm}$, its direction parallel to the axis along east to west. A wire carrying current of $7.0 \mathrm{~A}$ in the north to south direction passes through this region. What is the magnitude and direction of the force on the wire if,
(a) the wire intersects the axis,
(b) the wire is turned from $\mathrm{N}-\mathrm{S}$ to northeast-northwest direction.
(c) the wire in the $\mathrm{N}-\mathrm{S}$ direction is lowered from the axis by a distance of $6.0 \mathrm{~cm}$ ?
(a) the wire intersects the axis,
(b) the wire is turned from $\mathrm{N}-\mathrm{S}$ to northeast-northwest direction.
(c) the wire in the $\mathrm{N}-\mathrm{S}$ direction is lowered from the axis by a distance of $6.0 \mathrm{~cm}$ ?
Solution:
2438 Upvotes
Verified Answer
The magnetic field is in the direction east to west and in the cylindrical region of radius $10 \mathrm{~cm}$.
(a) A current carrying wire, intersects the axis.
Force on wire
$$
\begin{aligned}
F &=I B l=I B(2 r)=7 \times 1.5 \times 2 \times 1 \times 10^{-2} \\
&=2.1 \mathrm{~N} \text { upwards }
\end{aligned}
$$
(b) By turning the wire by an angle $45^{\circ}$ in NE and SW direction the force remain the same $f=2.1 \mathrm{~N}$.
(c) Now the wire is lowered from the axis by a distance of $6.0 \mathrm{~cm}$.
Length of wire inside cylindrical region is $16 \mathrm{~cm}$ now.
So, the force is $F=I B l=7 \times 1.5 \times 16 \times 10^{-2}$
$$
=1.68 \mathrm{~N}
$$
(a) A current carrying wire, intersects the axis.
Force on wire
$$
\begin{aligned}
F &=I B l=I B(2 r)=7 \times 1.5 \times 2 \times 1 \times 10^{-2} \\
&=2.1 \mathrm{~N} \text { upwards }
\end{aligned}
$$
(b) By turning the wire by an angle $45^{\circ}$ in NE and SW direction the force remain the same $f=2.1 \mathrm{~N}$.
(c) Now the wire is lowered from the axis by a distance of $6.0 \mathrm{~cm}$.
Length of wire inside cylindrical region is $16 \mathrm{~cm}$ now.
So, the force is $F=I B l=7 \times 1.5 \times 16 \times 10^{-2}$
$$
=1.68 \mathrm{~N}
$$
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