Question

Consider a circular loop of radius $R$ that is centred at the origin and lies in a plane with a normal in the direction given by polar angles $\phi_0$ and $\theta_0$. A current $I$ flows in the loop in an anti-clockwise sense with respect to the normal. The loop is subjected to an external field $\mathbf{B} = B_0[(1 - \beta y)\hat{\mathbf{x}} + (1 + \beta x)\hat{\mathbf{y}}]$ Find the total force on the loop. Hint: Note that the normal vector is given in spherical polars ($\hat{\mathbf{r}}_0$) so that the current element can be expressed in terms of $\hat{\theta}_0$ and $\hat{\phi}_0$. Also make use of $\hat{\mathbf{z}} \times \mathbf{r}$ and the identity for the triple vector product.

          Consider a circular loop of radius $R$ that is centred at the origin and lies in a plane with
a normal in the direction given by polar angles $\phi_0$ and $\theta_0$. A current $I$ flows in the loop in
an anti-clockwise sense with respect to the normal. The loop is subjected to an external
field
$\mathbf{B} = B_0[(1 - \beta y)\hat{\mathbf{x}} + (1 + \beta x)\hat{\mathbf{y}}]$
Find the total force on the loop.
Hint: Note that the normal vector is given in spherical polars ($\hat{\mathbf{r}}_0$) so that the current
element can be expressed in terms of $\hat{\theta}_0$ and $\hat{\phi}_0$. Also make use of $\hat{\mathbf{z}} \times \mathbf{r}$ and the identity
for the triple vector product.

Consider a circular loop of radius R that is centred at the origin and lies in a plane with
a normal in the direction given by polar angles ϕ0 and θ0. A current I flows in the loop in
an anti-clockwise sense with respect to the normal. The loop is subjected to an external
field
𝐁 = B0[(1 - β y)𝐱̂ + (1 + β x)𝐲̂]
Find the total force on the loop.
Hint: Note that the normal vector is given in spherical polars (𝐫̂0) so that the current
element can be expressed in terms of θ̂0 and ϕ̂0. Also make use of 𝐳̂×𝐫 and the identity
for the triple vector product.

Added by Isabel H.

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