问题 计算题

空间存在水平方向正交的匀强电场和匀强磁场,其大小分别为E=,B=1T,方向如图所示,有一质量m=2.0×10-6 kg,带正电荷量q=2.0×10-6 C的微粒,在此空间做直线运动,试求其速度大小和方向。

答案

解:先分析重力是否可以忽略。粒子重力G=mg=2.0×10-5 N,电场力F1=Eq=2×10-5 N。因重力与电场力的大小处在同一数量级,故重力不能忽略

再看粒子是否受到洛伦兹力,当粒子平行于磁感线方向运动时,不受洛伦兹力,但这样一来,粒子的运动方向与重力和电场力的合力方向垂直,它不可能做直线运动,与题目所设情境不符,故粒子一定受到洛伦兹力。可见,粒子运动时共受到三个力:重力G=mg,方向竖直向下;电场力F1=Eq,方向水平向右;洛伦兹力F2的大小与速度的大小有关,方向与速度的方向有关,只要确定了洛伦兹力的大小和方向,就可确定速度的大小和方向。那么是否存在这样一种情形,洛伦兹力与重力平衡,粒子沿电场方向做直线运动呢?其受力如图甲所示。仔细考虑一下,其实这种情形是不可能存在的,原因是随粒子速度的变化,洛伦兹力F2=qvB也将变化,从而竖直方向平衡被打破,可见粒子不可能做变速直线运动,而只能做匀速直线运动,其受力如图乙所示,由图可得

因为F2⊥v,所以θ=α=60°,qvB=2mg

由此得

即粒子将以20 m/s的速度,与电场方向成60°角斜向上做匀速直线运动

填空题
阅读理解

Shopping is not as simple as you may think! There are all sorts of tricks at play each time we reach out for that particular brand(品牌) of product on the shelf.

Colouring, for example, varies according to what the producers are trying to sell. Health foods are packaged(包装) in greens, yellows or browns because we think of these as healthy colours. Ice cream packets are often blue and expensive goods, like chocolates, are gold or silver.

When some kind of pain killer was brought out recently, researchers found that the colours turned the customers off because they made the product look weak and ineffective. Eventually, it came on the market in a dark blue and white package—blue because we think of it as safe, and white as calm.

The size of a product can attract a shopper. But quite often a bottle doesn’t contain as much as it appears to.

It is believed that the better-known companies spend, on average, 70 percent of the total cost of the product itself on packaging!

The most successful producers know that it’s not enough to have a good product. The founder of Pears soap, who for 25 years has used pretty little girls to promote (推销) their goods, came to the conclusion: “Any fool can make soap, but it takes a genius(天才) to sell it.”

小题1:Which of the following may trick a shopper into buying a product according to the text?

A.The cost of its package.

B.The price of the product.

C.The colour of its package.

D.The brand name of the product.小题2:The underlined part “the colours turned the customers off” (in Para.3) means that the colours _________.

A.attracted the customers strongly

B.caused the customers to lose interest

C.tricked the customers into shopping

D.had weak effects on the customers小题3:Which of the following is the key to the success in product sales?

A.The way to promote goods.

B.The discovery of a genius.

C.The team to produce a good product.

D.The brand name used by successful producers.小题4:According to the passage, we know that _________.

A.making soap is so easy that any fool in the world can make it.

B.greens, yellows or silver are considered to be healthy colours.

C.25 years ago, the founder of Pears soap was a pretty girl herself.

D.the size of a product can have an effect on the shoppers.小题5:Which of the following would be the best title for this text?

A.Choice of Good Products

B.Disadvantages of Products

C.Effect of Packaging on Shopping

D.Brand Names and Shopping Tricks