Question 221: Magnetism and Matter

Question

In a certain region static electric and magnetic fields exist. The magnetic field is given by $$\overrightarrow B  = {B_0}\left( {\widehat i + 2\widehat j - 4\widehat k} \right)$$ . If a test charge moving with a velocity $$\overrightarrow \upsilon   = {\upsilon _0}\left( {3\widehat i - \widehat j + 2\widehat k} \right)$$ experiences no force in that region, then the electric field in the region, in SI units, is :

Accepted Answer

Here test charge experience no net force,  So, sum of electric and magnetic field is zero.
$$	herefore\,\,\,$$ F
e
+ F
m
= 0
$$	herefore\,\,\,$$ F
e
= $$-$$ q ($$\overrightarrow v $$ $$ 	imes $$ $$\overrightarrow B)$$
= $$-$$ qB
0
$$\upsilon $$
0
[(3$$\widehat i$$ $$-$$ $$\widehat j$$ +  2$$\widehat k$$) $$ 	imes $$ ($$\widehat i$$ + 2$$\widehat j$$ $$-$$ 4$$\widehat k$$)]
= $$-$$ q$$\upsilon $$
0
B
0
(14$$\widehat j$$ + 7$$\widehat k$$)
Electric field produced by the charge q,
$$\overrightarrow E $$ = $${{\overrightarrow {{F_e}} } \over q}$$
= $${{ - q{\upsilon _0}{B_0}\left( {14\widehat j + 7\widehat k} ight)} \over q}$$
= $$-$$ $$\upsilon $$
0
B
0
(14 $${\widehat j}$$ + 7 $${\widehat k}$$)

Answer

$$\overrightarrow E  =  - {\upsilon _0}\,{B_0}\left( {3\widehat i - 2\widehat j - 4\widehat k} \right)$$

Answer

$$\overrightarrow E  =  - {\upsilon _0}\,{B_0}\left( {\widehat i + \widehat j + 7\widehat k} \right)$$

Answer

$$\overrightarrow E  = {\upsilon _0}\,{B_0}\left( {14\widehat j + 7\widehat k} \right)$$

Answer

$$\overrightarrow E  =  - {\upsilon _0}\,{B_0}\left( {14\widehat j + 7\widehat k} \right)$$

Magnetism and Matter

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